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Partition relations for countable topological spaces

1986
*
Journal of combinatorial theory. Series A
*

We consider

doi:10.1016/0097-3165(86)90059-2
fatcat:rcrlywtczvh4xoy7l3taefo3hy
*partition**relations**for*pairs of elements of a*countable**topological**space*.*For**spaces*with infinitely many nonempty derivatives a strong negative theorem is obtained. ... INTRODUCTION The purpose of this paper is to study some extensions of the*partition*calculus to*countable**topological**spaces*. ...##
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Partitioning topological spaces into countably many pieces

1987
*
Proceedings of the American Mathematical Society
*

*For*example, note that

*for*first

*countable*

*spaces*, this

*relation*just says that A is not (T-discrete. ... Consistently wi cannot replace u> + 1

*for*any X of size There have recently been several results regarding

*partitions*of

*topological*

*spaces*(

*for*a survey, see [2] ). ...

*For*example, note that

*for*first

*countable*

*spaces*, this

*relation*just says that A is not (T-discrete. ...

##
###
Page 833 of American Mathematical Society. Proceedings of the American Mathematical Society Vol. 4, Issue 5
[page]

1953
*
American Mathematical Society. Proceedings of the American Mathematical Society
*

(c) Every open covering of X has a

*partition*of unity subordinated to it. % As examples of Lindeléf*spaces*, let us mention second-*countable**spaces*(i.e.*spaces*with a*countable*base*for*the open sets) ... By a*partition*of unity on a*topological**space*X, we mean a family ® of continuous functions from X to the non-negative real numbers such that doves (x) =1*for*every xin X. ...##
###
On the Difference Hierarchy in Countably Based T0-Spaces

2008
*
Electronical Notes in Theoretical Computer Science
*

We discuss also a broad class of effective

doi:10.1016/j.entcs.2008.12.022
fatcat:nhetciwsl5fo5erktj35jlavu4
*topological**spaces*closely relevant to our study of the difference hierarchy and to computability in*topology*. ... theorem*for*kpartitions. ... The first class is closely*related*to separable metric*spaces*, i.e., metric*spaces*(X, d) having a*countable*dense set D ⊆ X. ...##
###
On the asymptotic relation of topological Z^2-actions

2015
*
Topological Methods in Nonlinear Analysis
*

*For*a

*topological*action Φ of a

*countable*amenable orderable group G on a compact metric

*space*we introduce a concept of the asymptotic

*relation*A(Φ) and we show that A(Φ) is non-trivial if the

*topological*... These results are generalizations of those of Blanchard, Host and Ruette ([3]) that concern the asymptotic

*relation*

*for*Z-actions. ... The aim of this paper is to extend the concept of asymptoticity to

*topological*actions of

*countable*amenable orderable groups. ...

##
###
Page 3888 of Mathematical Reviews Vol. , Issue 89G
[page]

1989
*
Mathematical Reviews
*

It is shown that (X,r) is
an (L2)-

*space*(i.e., the set cl{x} —{y € X:x Ecl{y}, y € cl{x}} is closed*for*each x € X) if and only if (X, felt) is a*partition**space*. ...*For*any first*countable*compact Hausdorff*space*X with a PPC base, a zero-dimensional first*countable*compact Hausdorff*space*Y is con- structed which can be mapped continuously onto X¥. ...##
###
Page 763 of Mathematical Reviews Vol. 46, Issue 3
[page]

1973
*
Mathematical Reviews
*

Wong, Yim-ming

*Partition**spaces*. Yokohama Math. J. 20 (1972), 1-34. Let X be a*topological**space*and R an equivalence*relation*on X. ... The quotient*space*X/R is called a*partition**space*4457 _when R-*related*points of X belong to the same open sets | of X. ...##
###
On the structure of zerodimensional spaces

1975
*
Indagationes Mathematicae (Proceedings)
*

*For*each n let sla be a

*partition*of X into (

*countably*many!) clopen sets which contains either D, or a

*partition*of D, into clopen sets, and which refines an-i. ... UNIFORM STRUCTURES THEOREM 18: X is a non-archimedean

*topological*

*space*if and only if the

*topology*is induced by a uniformity 12 on X which has a base 93 of equivalence

*relations*such that

*for*any pair ...

##
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TheD-Property of Finite Unions oft-Metrizable Spaces and Certain Function Spaces

2013
*
Journal of Function Spaces and Applications
*

It is shown that a

doi:10.1155/2013/612954
fatcat:itr2b6zvfvfivof57soxkvhkx4
*space*of*countable*tightness is aD-*space*provided that it is the union of finitely manyt-metrizable subspaces, or function spacesCp(Xi)where eachXiis LindelöfΣ. ... The additivity ofD-property is studied ont-metrizable*spaces*and certain function*spaces*. ... A*space*has*countable*tightness if ∈ implies that ∈*for*some*countable*subset of . Definition 6 (see [21] ). The*topology*of ( , ) is Definition 7 (see [22] ). ...##
###
Page 353 of Mathematical Reviews Vol. , Issue 94a
[page]

1994
*
Mathematical Reviews
*

The cardinal function e(X) = min{|A|: A is xcc in X} is defined

*for**countably*compact*spaces*X. Several facts are noted involving extra*countably*compact subspaces, dense subspaces and e(X). ... A number of*related*questions are listed at the end.” ...##
###
Partitioning the pairs and triples of topological spaces

1990
*
Topology and its Applications
*

We carry out the task given by the title, introduce a combinatorial princip;', and use it to prove X f (top o + 1):

doi:10.1016/0166-8641(90)90103-9
fatcat:qakd7ptw2nh5hedxvjnw2ecura
*for*ait*spaces*X, X + ( Y)',*for*a11*spaces*X where Y is any nondiscrete*countable**space*... , and*related*results. ... The*partition*calculus*for**topological**spaces*arises from the ordinary*partition*calculus*for*cardinals, as expounded,*for*example, in [2] . ...##
###
Upper semi-continuity of entropy in non-compact settings
[article]

2018
*
arXiv
*
pre-print

We prove that the entropy map

arXiv:1809.10022v2
fatcat:23hgk7ylbrg3vbetc7jvgiqzmu
*for**countable*Markov shifts of finite entropy is upper semi-continuous at ergodic measures. Note that the phase*space*is non-compact. ... We also discuss the*related*problem of existence of measures of maximal entropy. ... This is no longer true*for**countable*generating*partitions*. Krieger [Kr] constructed a finite generating*partition**for*each ergodic measure. ...##
###
Classes of barren extensions
[article]

2020
*
arXiv
*
pre-print

This begged the question of how important the Ramseyness of U is

arXiv:1911.06936v3
fatcat:5zuvsfybo5g45cjtbtbvnw76qa
*for*these results. ... Moreover, under an additional assumption, they proved that this generic extension preserves all strong*partition*cardinals. ... The authors would like to thank Carlos DiPrisco, Paul Larson, and Adrian Mathias*for*their generous discussions which greatly benefited this paper, and the anonymous referee*for*ways to improve clarity ...##
###
Blackwell Spaces and -Approximations of Markov Chains

2011
*
International Journal of Stochastic Analysis
*

On a weakly Blackwell

doi:10.1155/2011/801303
fatcat:tzboumdnkvgpzijrv4i2bt5gwy
*space*we show how to define a Markov chain approximating problem,*for*the target problem. ... He wishes to thank*for*the warm hospitality. ... generated by a*countable**partition*of X. ...##
###
Completeness Properties of the open-point and bi-point-open topologies on C(X)
[article]

2016
*
arXiv
*
pre-print

This paper studies various completeness properties of the open-point and bi-point-open

arXiv:1607.01491v1
fatcat:ngjgsx67tbfzpgsityydrfjn2u
*topologies*on the*space*C(X) of all real-valued continuous functions on a Tychonoff*space*X. ... The properties range from complete metrizability to the Baire*space*property. ... (j) X is a*countable*discrete*space*. bi-point-open*topology*on C(X) is the join of the point-open*topology*p and the open-point*topology*h. ...
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