Research articles

Work in Progress

August 2016
Jan Pachl and Juris Steprans
Centres of Banach algebra actions

The topological centre of a Banach algebra action is described and examined for the special case of a group acting on a set. A construction of Foreman is modified in this context.
July 2016
Juris Steprans
Complexity of the weakly almost periodic functions

It is shown that the set of weakly approximately periodic functions on various abelian groups is a complete co-analytic set.
June 2016
Saharon Shelah and Juris Steprans
Universal Graphs on omega_1

Iterations of various well know reals are used together with the P-Ideal dichotomy arguments to construct models of the failure of the Continuum Hypothesis together with the existence of a universal graph on omega_1.
August 2011
J. Steprans

Under Martin's Axiom the w*-closure of fewer than continuum singular elements of L1** is contained in the set of singular elements of L1**.
June 2011
D. Raghavan and J. Steprans

The amenability character of a Banach algebra is defined and some elementary observations about it are made. In particular, it is shown that C(X) has countable amenability character if and only if X is metrizable.
May 2011
J. Steprans

A question of V. Pestov on amenable actions is answered using a construction of M. Foreman.
May 2011
J. Steprans

These are slides of a four lecture series on amenability presented at the Young Set Theorists meeting in Bonn in 2011. The last lecture contains joint work with D.Raghavan extending Foreman's group construction

Reviewed Articles

July 2016 Jan Pachl and Juris Steprans
Convolution continuity and SIN groups

The joint and separate continuity properties of the convolution operation on LUC(G) are studied for G a SIN group.
MR3549381
When automorphisms of P(kappa)/fin are trivial off a small set
Saharon Shelah and Juris Steprans
Fund. Math.   235
 167--181  (2016)
http://dx.doi.org/10.4064/fm222-2-2016
MR3451936
Proof of the {G}hahramani-{L}au conjecture
V. Losert and M. Neufang and J. Pachl and J. Steprans
Adv. Math.  290  709--738  (2016)
http://dx.doi.org/10.1016/j.aim.2015.12.004
MR3401904
Non-trivial automorphisms of {\scrP(\BbbN)/[\BbbN]<ℵ0} from variants of small dominating number
S. Shelah and J. Steprāns
Eur. J. Math.  1  534--544  (2015)
http://dx.doi.org/10.1007/s40879-015-0058-0

MR3236763
Applications of harmonic analysis to the theory of cardinal invariants
Juris Steprans
CMS Notes  46  12--13  (2014)

MR3268711
Universal functions
P. B. Larson and A. W. Miller and J. Steprāns and W. A. R. Weiss
Fund. Math.  227  197--246  (2014)
http://dx.doi.org/10.4064/fm227-3-1

MR3176143
Haar null sets and the consistent reflection of non-meagreness
M. Elekes and J. Steprāns
Canad. J. Math.  66  303--322  (2014)
http://dx.doi.org/10.4153/CJM-2012-058-5

MR3150724
Splitting families and complete separability
H. Mildenberger and D. Raghavan and J. Steprans
Canad. Math. Bull.  57  119--124  (2014)
http://dx.doi.org/10.4153/CMB-2013-027-2

MR2991425
Semigroups in which all strongly summable ultrafilters are sparse
N. Hindman and J. Steprans and D. Strauss
New York J. Math.  18  835--848  (2012)
http://nyjm.albany.edu:8000/j/2012/18_835.html

MR2926314
Continuous maps on Aronszajn trees
K. Kunen and J. A. Larson and J. Steprāns
Order  29  311--316  (2012)
http://dx.doi.org/10.1007/s11083-011-9205-5

MR3295936
Sets and extensions in the twentieth century
Juris Steprans
History of the continuum in the 20th century  73 to 144  (2012)

MR2901224
Maximal functions and the additivity of various families of null sets
J. Steprāns
Trans. Amer. Math. Soc.  364  3555--3584  (2012)
http://dx.doi.org/10.1090/S0002-9947-2012-05402-X

MR2805847
Masas in the {C}alkin algebra without the continuum hypothesis
S. Shelah and J. Steprāns
J. Appl. Anal.  17  69--89  (2011)
http://dx.doi.org/10.1515/JAA.2011.004

MR2658145
The commutant of L(H) in its ultrapower may or may not be trivial
Ilijas Farah, N. Christopher Phillips, and Juris Steprans
Mathematische Annalen  347  839--857  (2010)
DOI: 10.1007/s00208-009-0448-z
MR2467209
Analytic and coanalytic families of almost disjoint functions
B. Kastermans and J. Steprans and Y. Zhang
J. Symbolic Logic  73  1158--1172  (2008)
http://projecteuclid.org/getRecord?id=euclid.jsl/1230396911

MR2462464
Chasing Silver
A. Roslanowski and J. Steprans
Canad. Math. Bull.  51  593--603  (2008)
DOI: 10.4153/CMB-2008-059-2

MR2457482
The consistency of b=κ and s=κ+
V. Fischer and J. Steprans
Fund. Math.  201  283--293  (2008)
DOI: 10.4064/fm201-3-5

MR2353856
Possible cardinalities of maximal abelian subgroups of quotients of permutation groups of the integers
S. Shelah and J. Steprans
Fund. Math.  196  197--235  (2007)
DOI: 10.4064/fm196-3-1

MR2258628
Products of sequential CLP-compact spaces are CLP-compact
J. Steprans
Ann. Pure Appl. Logic  143  155--157  (2006)
DOI: 10.1016/j.apal.2005.03.005

MR2224048
The number of translates of a closed nowhere dense set required to cover a Polish group
A. W. Miller and J. Steprans
Ann. Pure Appl. Logic  140  52--59  (2006)
DOI: 10.1016/j.apal.2005.09.010

MR2214123
Chains of Baire class 1 functions and various notions of special trees
M. Elekes and J. Steprans
Israel J. Math.  151  179--187  (2006)
DOI: 10.1007/BF02777361

MR2198711
Geometric cardinal invariants, maximal functions and a measure theoretic pigeonhole principle
J. Steprans
Bull. Symbolic Logic  11  517--525  (2005)
http://projecteuclid.org/getRecord?id=euclid.bsl/1130335207

MR2167583
Many quotient algebras of the integers modulo co-analytic ideals
J. Steprans
Contemp. Math. Logic and its applications  380  271--281  (2005)

MR2128705
Comparing the uniformity invariants of null sets for different measures
S. Shelah and J. Steprans
Adv. Math.  192  403--426  (2005)
DOI: 10.1016/j.aim.2004.04.010

MR2092071
Complete Erdos space is unstable
J. J. Dijkstra and J. Van Mill and J. Steprans
Math. Proc. Cambridge Philos. Soc.  137  465--473  (2004)
DOI: 10.1017/S0305004104007996

MR2071696
Less than 2ω many translates of a compact nullset may cover the real line
M. Elekes and J. Steprans
Fund. Math.  181  89--96  (2004)
DOI: 10.4064/fm181-1-4

MR1990584
The autohomeomorphism group of the Cech-Stone compactification of the integers
J. Steprans
Trans. Amer. Math. Soc.  355  4223--4240 (electronic)  (2003)
DOI: 10.1090/S0002-9947-03-03329-4

MR1896046
Martin's axiom is consistent with the existence of nowhere trivial automorphisms
S. Shelah and J. Steprans
Proc. Amer. Math. Soc.  130  2097--2106 (electronic)  (2002)
DOI: 10.1090/S0002-9939-01-06280-3

MR2032852
The uniformity invariants of the ideal of null sets in separable metric spaces
J. Steprans
Topology Proc.  26  811--818  (2001/02)

MR1923169
The almost disjointness cardinal invariant in the quotient algebra of the rationals modulo the nowhere dense subsets
J. Steprans
Real Anal. Exchange  27  795--800  (2001/02)

MR1856740
Cofinitary groups, almost disjoint and dominating families
M. Hrusak and J. Steprans and Y. Zhang
J. Symbolic Logic  66  1259--1276  (2001)
DOI: 10.2307/2695105

MR1855551
Cardinal invariants related to sequential separability
M. Hrusak and J. Steprans
S\=urikaisekikenky\=usho K\=oky\=uroku    66--74  (2001)

MR1833473
The covering numbers of Mycielski ideals are all equal
S. Shelah and J. Steprans
J. Symbolic Logic  66  707--718  (2001)
DOI: 10.2307/2695039

MR1733805
Restricted compactness properties and their preservation under products
J. Steprans and A. P. Sostak
Topology Appl.  101  213--229  (2000)
DOI: 10.1016/S0166-8641(98)00126-6

MR1777780
Unions of rectifiable curves in Euclidean space and the covering number of the meagre ideal
J. Steprans
J. Symbolic Logic  64  701--726  (1999)
DOI: 10.2307/2586494

MR1473455
Decomposing Euclidean space with a small number of smooth sets
J. Steprans
Trans. Amer. Math. Soc.  351  1461--1480  (1999)
DOI: 10.1090/S0002-9947-99-02197-2

MR1610762
Orthogonal families of real sequences
A. W. Miller and J. Steprans
J. Symbolic Logic  63  29--49  (1998)
DOI: 10.2307/2586584

MR1625478
Maximal filters, continuity and choice principles
H. Herrlich and J. Steprans
Quaestiones Math.  20  697--705  (1997)

MR1450995
Gδ-sets in topological spaces and games
W. Just and M. Scheepers and J. Steprans and P. J. Szeptycki
Fund. Math.  153  41--58  (1997)

MR1433612
Hausdorff capacity and Lebesgue measure
T. S. Salisbury and J. Steprans
Real Anal. Exchange  22  265--278  (1996/97)

MR1405489
Reaping numbers of Boolean algebras
A. Dow and J. Steprans and S. Watson
Bull. London Math. Soc.  28  591--599  (1996)
DOI: 10.1112/blms/28.6.591

MR1367140
Cardinal invariants associated with Hausdorff capacities
J. Steprans
192  147--184  (1996)

MR1314977
Sums of Darboux and continuous functions
J. Steprans
Fund. Math.  146  107--120  (1995)

MR1301530
Mutually complementary families of T1 topologies, equivalence relations and partial orders
J. Steprans and S. Watson
Proc. Amer. Math. Soc.  123  2237--2249  (1995)
DOI: 10.2307/2160963

MR1303686
A topological Banach fixed point theorem for compact Hausdorff spaces
J. Steprans and S. Watson and W. Just
Canad. Math. Bull.  37  552--555  (1994)

MR1297403
Decomposing Baire class 1 functions into continuous functions
S. Shelah and J. Steprans
Fund. Math.  145  171--180  (1994)

MR1271551
Somewhere trivial autohomeomorphisms
S. Shelah and J. Steprans
J. London Math. Soc. (2)  49  569--580  (1994)

MR1271434
Erratum: ``Maximal chains in ωω and ultrapowers of the integers'' [Arch. Math. Logic {\bf 32} (1993), no.\ 5, 305--319; {MR}1223393 (94g:03094)]
S. Shelah and J. Steprans
Arch. Math. Logic  33  167--168  (1994)
DOI: 10.1007/BF01352936

MR1261556
The σ-linkedness of the measure algebra
A. Dow and J. Steprans
Canad. Math. Bull.  37  42--45  (1994)

MR1259349
Homogeneous almost disjoint families
S. Shelah and J. Steprans
Algebra Universalis  31  196--203  (1994)
DOI: 10.1007/BF01236517

MR1253008
Dominating functions and graphs
R. Diestel and S. Shelah and J. Steprans
J. London Math. Soc. (2)  49  16--24  (1994)

MR1252708
The evolution of integration
A. Shenitzer and J. Steprans
Amer. Math. Monthly  101  66--72  (1994)
DOI: 10.2307/2325128

MR1253921
A very discontinuous Borel function
J. Steprans
J. Symbolic Logic  58  1268--1283  (1993)
DOI: 10.2307/2275142

MR1239060
Martin's axiom and the transitivity of Pc-points
J. Steprans
Israel J. Math.  83  257--274  (1993)
DOI: 10.1007/BF02784054

MR1234290
Combinatorial consequences of adding Cohen reals
J. Steprans
6  583--617  (1993)

MR1229497
Continuous colourings of closed graphs
A. Krawczyk and J. Steprans
Topology Appl.  51  13--26  (1993)
DOI: 10.1016/0166-8641(93)90011-2

MR1223393
Maximal chains in ωω and ultrapowers of the integers
S. Shelah and J. Steprans
Arch. Math. Logic  32  305--319  (1993)
DOI: 10.1007/BF01409965

MR1217174
Combinatorial properties of the ideal P2
J. Cichon and A. Roslanowski and J. Steprans and B. Weglorz
J. Symbolic Logic  58  42--54  (1993)
DOI: 10.2307/2275322

MR1186465
Countable Frechet α1-spaces may be first countable
A. Dow and J. Steprans
Arch. Math. Logic  32  33--50  (1992)
DOI: 10.1007/BF01270393

MR1168663
Topological invariants in the Cohen model
J. Steprans
Topology Appl.  45  85--101  (1992)
DOI: 10.1016/0166-8641(92)90050-A

MR1206463
Almost disjoint families of paths in lattice grids
J. Steprans
Topology Proc.  16  185--200  (1991)

MR1078638
Steprans' problems
J. Steprans
  13--20  (1990)

MR1002627
Nontrivial homeomorphisms of βN\N without the continuum hypothesis
S. Shelah and J. Steprans
Fund. Math.  132  135--141  (1989)

MR985683
A model in which countable Frechet α1-spaces are first countable
A. Dow and J. Steprans
Math. Proc. Cambridge Philos. Soc.  105  473--480  (1989)

MR962545
Destroying precaliber ℵ1: an application of a &Delta-system lemma for closed sets
J. Steprans and S. Watson
Fund. Math.  129  223--229  (1988)

MR958051
A Banach space on which there are few operators
S. Shelah and J. Steprans
Proc. Amer. Math. Soc.  104  101--105  (1988)
DOI: 10.2307/2047469

MR935111
PFA implies all automorphisms are trivial
S. Shelah and J. Steprans
Proc. Amer. Math. Soc.  104  1220--1225  (1988)
DOI: 10.2307/2047617

MR932979
Some results on CDH spaces. I
J. Steprans and H. X. Zhou
Topology Appl.  28  147--154  (1988)
DOI: 10.1016/0166-8641(88)90006-5

MR932978
Cellularity of first countable spaces
J. Steprans and S. Watson
Topology Appl.  28  141--145  (1988)
DOI: 10.1016/0166-8641(88)90005-3

MR887767
Homeomorphisms of manifolds with prescribed behaviour on large dense sets
J. Steprans and W. S. Watson
Bull. London Math. Soc.  19  305--310  (1987)
DOI: 10.1112/blms/19.4.305

MR887554
Extraspecial p-groups
S. Shelah and J. Steprans
Ann. Pure Appl. Logic  34  87--97  (1987)
DOI: 10.1016/0168-0072(87)90041-8

MR801424
Strong Q-sequences and variations on Martin's axiom
J. Steprans
Canad. J. Math.  37  730--746  (1985)

MR770551
A characterization of free abelian groups
J. Steprans
Proc. Amer. Math. Soc.  93  347--349  (1985)
DOI: 10.2307/2044776

MR769852
The number of directed sets
K. J. Devlin and J. Steprans and W. S. Watson
Rend. Circ. Mat. Palermo (2)    31--41  (1984)

MR743378
The number of submodules
J. Steprans
Proc. London Math. Soc. (3)  49  183--192  (1984)
DOI: 10.1112/plms/s3-49.1.183

MR1540295
Problems and Solutions: Solutions of Advanced Problems: 6380
J. Steprans
Amer. Math. Monthly  90  649  (1983)
http://links.jstor.org/sici?sici=0002-9890(198311)90:9<649:6>2.0.CO;2-K&origin=MSN

MR1539901
Problems and Solutions: Advanced Problems: 6380-6382
J. Steprans and W. W. Meyer and H. Lam
Amer. Math. Monthly  89  214  (1982)
DOI: 10.2307/2320210

MR633292
Cardinal arithmetic and ℵ1-Borel sets
J. Steprans
Proc. Amer. Math. Soc.  84  121--126  (1982)
DOI: 10.2307/2043823

MR612014
Trees and continuous mappings into the real line
J. Steprans
Topology Appl.  12  181--185  (1981)
DOI: 10.1016/0166-8641(81)90019-5