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A game and its relation to netweight and D-spaces

Gary Gruenhage, Paul Szeptycki (2011)

Commentationes Mathematicae Universitatis Carolinae

We introduce a two player topological game and study the relationship of the existence of winning strategies to base properties and covering properties of the underlying space. The existence of a winning strategy for one of the players is conjectured to be equivalent to the space have countable network weight. In addition, connections to the class of D-spaces and the class of hereditarily Lindelöf spaces are shown.

A note on k-c-semistratifiable spaces and strong β -spaces

Li-Xia Wang, Liang-Xue Peng (2011)

Mathematica Bohemica

Recall that a space X is a c-semistratifiable (CSS) space, if the compact sets of X are G δ -sets in a uniform way. In this note, we introduce another class of spaces, denoting it by k-c-semistratifiable (k-CSS), which generalizes the concept of c-semistratifiable. We discuss some properties of k-c-semistratifiable spaces. We prove that a T 2 -space X is a k-c-semistratifiable space if and only if X has a g function which satisfies the following conditions: (1) For each x X , { x } = { g ( x , n ) : n } and g ( x , n + 1 ) g ( x , n ) for each n . (2) If a...

A note on monotone countable paracompactness

Ge Ying, Chris Good (2001)

Commentationes Mathematicae Universitatis Carolinae

We show that a space is MCP (monotone countable paracompact) if and only if it has property ( * ) , introduced by Teng, Xia and Lin. The relationship between MCP and stratifiability is highlighted by a similar characterization of stratifiability. Using this result, we prove that MCP is preserved by both countably biquotient closed and peripherally countably compact closed mappings, from which it follows that both strongly Fréchet spaces and q-space closed images of MCP spaces are MCP. Some results on...

Decreasing (G) spaces

Ian Stares (1998)

Commentationes Mathematicae Universitatis Carolinae

We consider the class of decreasing (G) spaces introduced by Collins and Roscoe and address the question as to whether it coincides with the class of decreasing (A) spaces. We provide a partial solution to this problem (the answer is yes for homogeneous spaces). We also express decreasing (G) as a monotone normality type condition and explore the preservation of decreasing (G) type properties under closed maps. The corresponding results for decreasing (A) spaces are unknown.

Equiconnected spaces and Baire classification of separately continuous functions and their analogs

Olena Karlova, Volodymyr Maslyuchenko, Volodymyr Mykhaylyuk (2012)

Open Mathematics

We investigate the Baire classification of mappings f: X × Y → Z, where X belongs to a wide class of spaces which includes all metrizable spaces, Y is a topological space, Z is an equiconnected space, which are continuous in the first variable. We show that for a dense set in X these mappings are functions of a Baire class α in the second variable.

Hyperspaces of CW-complexes

Bao-Lin Guo, Katsuro Sakai (1993)

Fundamenta Mathematicae

It is shown that the hyperspace of a connected CW-complex is an absolute retract for stratifiable spaces, where the hyperspace is the space of non-empty compact (connected) sets with the Vietoris topology.

Les stratifiés topologiques et les polyèdres

Laurent Siebenmann (1973)

Annales de l'institut Fourier

On conjecture que certains espaces localement étoilés admettent toujours une jolie stratification naturelle, et deviennent ainsi ce qu’on appelle des C S ensembles. On cite quelques propriétés agréables des C S ensembles, et quelques exemples exotiques qui distinguent les C S ensembles, les espaces triangulables, et les espaces localement triangulables.

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