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Partition relations for countable topological spaces

James E Baumgartner
1986 Journal of combinatorial theory. Series A  
We consider 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.  ... 
doi:10.1016/0097-3165(86)90059-2 fatcat:rcrlywtczvh4xoy7l3taefo3hy

Partitioning topological spaces into countably many pieces

P. Komj{áth, W. Weiss
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.  ... 
doi:10.1090/s0002-9939-1987-0911048-6 fatcat:uycv4itx7vdufikgvzdtzfkc2e

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

Victor Selivanov
2008 Electronical Notes in Theoretical Computer Science  
We discuss also a broad class of effective 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.  ... 
doi:10.1016/j.entcs.2008.12.022 fatcat:nhetciwsl5fo5erktj35jlavu4

On the asymptotic relation of topological Z^2-actions

Wojciech Bułatek, Brunon Kamiński, Jerzy Szymański
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.  ... 
doi:10.12775/tmna.2015.086 fatcat:a7zecwx26vcz5mzf5dylvg6iue

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

P Nyikos, H.C Reichel
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  ... 
doi:10.1016/1385-7258(75)90024-4 fatcat:ph5yg3inhval3nmmo4srwapa44

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

Xin Zhang, Hongfeng Guo
2013 Journal of Function Spaces and Applications  
It is shown that a 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] ).  ... 
doi:10.1155/2013/612954 fatcat:itr2b6zvfvfivof57soxkvhkx4

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

A. Hajnal, I. Juhász, W. Weiss
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): 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] .  ... 
doi:10.1016/0166-8641(90)90103-9 fatcat:qakd7ptw2nh5hedxvjnw2ecura

Upper semi-continuity of entropy in non-compact settings [article]

Godofredo Iommi, Mike Todd, Aníbal Velozo
2018 arXiv   pre-print
We prove that the entropy map 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.  ... 
arXiv:1809.10022v2 fatcat:23hgk7ylbrg3vbetc7jvgiqzmu

Classes of barren extensions [article]

Natasha Dobrinen, Daniel Hathaway
2020 arXiv   pre-print
This begged the question of how important the Ramseyness of U is 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  ... 
arXiv:1911.06936v3 fatcat:5zuvsfybo5g45cjtbtbvnw76qa

Blackwell Spaces and -Approximations of Markov Chains

Giacomo Aletti, Diane Saada
2011 International Journal of Stochastic Analysis  
On a weakly Blackwell 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.  ... 
doi:10.1155/2011/801303 fatcat:tzboumdnkvgpzijrv4i2bt5gwy

Completeness Properties of the open-point and bi-point-open topologies on C(X) [article]

Anubha Jindal, R. A. McCoy, S. Kundu, Varun Jindal
2016 arXiv   pre-print
This paper studies various completeness properties of the open-point and bi-point-open 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.  ... 
arXiv:1607.01491v1 fatcat:ngjgsx67tbfzpgsityydrfjn2u
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