All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 4 Next

Displaying 61 – 80 of 477

Showing per page

An observation on spaces with a zeroset diagonal

Wei-Feng Xuan (2020)

Mathematica Bohemica

We say that a space X has the discrete countable chain condition (DCCC for short) if every discrete family of nonempty open subsets of X is countable. A space X has a zeroset diagonal if there is a continuous mapping f : X 2 → [ 0 , 1 ] with Δ X = f - 1 ( 0 ) , where Δ X = { ( x , x ) : x ∈ X } . In this paper, we prove that every first countable DCCC space with a zeroset diagonal has cardinality at most 𝔠 .

Applications of limited information strategies in Menger's game

Steven Clontz (2017)

Commentationes Mathematicae Universitatis Carolinae

As shown by Telgársky and Scheepers, winning strategies in the Menger game characterize σ -compactness amongst metrizable spaces. This is improved by showing that winning Markov strategies in the Menger game characterize σ -compactness amongst regular spaces, and that winning strategies may be improved to winning Markov strategies in second-countable spaces. An investigation of 2-Markov strategies introduces a new topological property between σ -compact and Menger spaces.

Aull-paracompactness and strong star-normality of subspaces in topological spaces

Kaori Yamazaki (2004)

Commentationes Mathematicae Universitatis Carolinae

We prove for a subspace Y of a T 1 -space X , Y is (strictly) Aull-paracompact in X and Y is Hausdorff in X if and only if Y is strongly star-normal in X . This result provides affirmative answers to questions of A.V. Arhangel’skii–I.Ju. Gordienko [3] and of A.V. Arhangel’skii [2].

Base-base paracompactness and subsets of the Sorgenfrey line

Strashimir G. Popvassilev (2012)

Mathematica Bohemica

A topological space X is called base-base paracompact (John E. Porter) if it has an open base ℬ such that every base ℬ ' ⊆ ℬ has a locally finite subcover 𝒞 ⊆ ℬ ' . It is not known if every paracompact space is base-base paracompact. We study subspaces of the Sorgenfrey line (e.g. the irrationals, a Bernstein set) as a possible counterexample.

Borel extensions of Baire measures

J. Aldaz (1997)

Fundamenta Mathematicae

We show that in a countably metacompact space, if a Baire measure admits a Borel extension, then it admits a regular Borel extension. We also prove that under the special axiom ♣ there is a Dowker space which is quasi-Mařík but not Mařík, answering a question of H. Ohta and K. Tamano, and under P(c), that there is a Mařík Dowker space, answering a question of W. Adamski. We answer further questions of H. Ohta and K. Tamano by showing that the union of a Mařík space and a compact space is Mařík,...

Cardinalities of DCCC normal spaces with a rank 2-diagonal

Wei-Feng Xuan, Wei-Xue Shi (2016)

Mathematica Bohemica

A topological space X has a rank 2-diagonal if there exists a diagonal sequence on X of rank 2 , that is, there is a countable family { 𝒰 n : n ∈ ω } of open covers of X such that for each x ∈ X , { x } = ⋂ { St 2 ( x , 𝒰 n ) : n ∈ ω } . We say that a space X satisfies the Discrete Countable Chain Condition (DCCC for short) if every discrete family of nonempty open subsets of X is countable. We mainly prove that if X is a DCCC normal space with a rank 2-diagonal, then the cardinality of X is at most 𝔠 . Moreover, we prove that if X is a first countable...

Čech complete nearness spaces

H. L. Bentley, Worthen N. Hunsaker (1992)

Commentationes Mathematicae Universitatis Carolinae

We study Čech complete and strongly Čech complete topological spaces, as well as extensions of topological spaces having these properties. Since these two types of completeness are defined by means of covering properties, it is quite natural that they should have a convenient formulation in the setting of nearness spaces and that in that setting these formulations should lead to new insights and results. Our objective here is to give an internal characterization of (and to study) those nearness...

Currently displaying 61 – 80 of 477