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Separable extensions of first countable spaces

Eric van Douwen, Teodor Przymusiński (1980)

Fundamenta Mathematicae

Sequentially continuous mappings of product spaces

D. V. Choodnovsky (1977/1978)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

Seven characterizations of non-meager 𝖯-filters

Kenneth Kunen, Andrea Medini, Lyubomyr Zdomskyy (2015)

Fundamenta Mathematicae

We give several topological/combinatorial conditions that, for a filter on ω, are equivalent to being a non-meager -filter. In particular, we show that a filter is countable dense homogeneous if and only if it is a non-meager -filter. Here, we identify a filter with a subspace of $2^{ω}$ through characteristic functions. Along the way, we generalize to non-meager -filters a result of Miller (1984) about -points, and we employ and give a new proof of results of Marciszewski (1998). We also employ a theorem...

Sixty questions on regular not paracompact spaces

Watson, Stephen W. (1984)

Proceedings of the 11th Winter School on Abstract Analysis

Solution of Kuratowski's problem on function having the Baire property, I

Ryszard Frankiewicz, Kenneth Kunen (1987)

Fundamenta Mathematicae

Some conditions under which a uniform space is fine

Umberto Marconi (1993)

Commentationes Mathematicae Universitatis Carolinae

Let $X$ be a uniform space of uniform weight $μ$ . It is shown that if every open covering, of power at most $μ$ , is uniform, then $X$ is fine. Furthermore, an $ω_{μ}$ -metric space is fine, provided that every finite open covering is uniform.

Some new versions of an old game

Vladimir Vladimirovich Tkachuk (1995)

Commentationes Mathematicae Universitatis Carolinae

The old game is the point-open one discovered independently by F. Galvin [7] and R. Telgársky [17]. Recall that it is played on a topological space $X$ as follows: at the $n$ -th move the first player picks a point $x_{n} \in X$ and the second responds with choosing an open $U_{n} ∋ x_{n}$ . The game stops after $ω$ moves and the first player wins if $\cup {U_{n} : n \in ω} = X$ . Otherwise the victory is ascribed to the second player. In this paper we introduce and study the games $θ$ and $Ω$ . In $θ$ the moves are made exactly as in the point-open game, but the...

Some topological consequences of the Product Measure Extension Axiom

Heikki Junnila (1983)

Fundamenta Mathematicae

Spaces of continuous functions, box products and almost- $ω$ -resolvable spaces

Angel Tamariz-Mascarúa, H. Villegas-Rodríguez (2002)

Commentationes Mathematicae Universitatis Carolinae

A dense-in-itself space $X$ is called $C_{□}$ -discrete if the space of real continuous functions on $X$ with its box topology, $C_{□} (X)$ , is a discrete space. A space $X$ is called almost- $ω$ -resolvable provided that $X$ is the union of a countable increasing family of subsets each of them with an empty interior. We analyze these classes of spaces by determining their relations with $κ$ -resolvable and almost resolvable spaces. We prove that every almost- $ω$ -resolvable space is $C_{□}$ -discrete, and that these classes coincide in...

Displaying 1 – 13 of 13

Separable extensions of first countable spaces

Sequentially continuous mappings of product spaces

Seven characterizations of non-meager 𝖯-filters

Sixty questions on regular not paracompact spaces

Solution of Kuratowski's problem on function having the Baire property, I

Some conditions under which a uniform space is fine

Some new versions of an old game

Some topological consequences of the Product Measure Extension Axiom

Spaces of continuous functions, box products and almost- $ω$ -resolvable spaces

Spaces of urelements

Spaces with a locally countable $s n$ -network.

Squares of Q sets

Strongly discrete subsets in ω*

Currently displaying 1 – 13 of 13