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Convergent Filter Bases

Roland Coghetto (2015)

Formalized Mathematics

We are inspired by the work of Henri Cartan [16], Bourbaki [10] (TG. I Filtres) and Claude Wagschal [34]. We define the base of filter, image filter, convergent filter bases, limit filter and the filter base of tails (fr: filtre des sections).

Countable compactness and p -limits

Salvador García-Ferreira, Artur Hideyuki Tomita (2001)

Commentationes Mathematicae Universitatis Carolinae

For ∅ ≠ M ⊆ ω * , we say that X is quasi M -compact, if for every f : ω → X there is p ∈ M such that f ¯ ( p ) ∈ X , where f ¯ is the Stone-Čech extension of f . In this context, a space X is countably compact iff X is quasi ω * -compact. If X is quasi M -compact and M is either finite or countable discrete in ω * , then all powers of X are countably compact. Assuming C H , we give an example of a countable subset M ⊆ ω * and a quasi M -compact space X whose square is not countably compact, and show that in a model of A. Blass and S. Shelah every quasi...

Countable fan-tightness versus countable tightness

Aleksander V. Arhangel'skii, Angelo Bella (1996)

Commentationes Mathematicae Universitatis Carolinae

Countable tightness is compared to the stronger notion of countable fan-tightness. In particular, we prove that countable tightness is equivalent to countable fan-tightness in countably compact regular spaces, and that countable fan-tightness is preserved by pseudo-open compact mappings. We also discuss the behaviour of countable tightness and of countable fan-tightness under the product operation.

Countable sums and products of Loeb and selective metric spaces

Horst Herrlich, Kyriakos Keremedis, Eleftherios Tachtsis (2005)

Commentationes Mathematicae Universitatis Carolinae

We investigate the role that weak forms of the axiom of choice play in countable Tychonoff products, as well as countable disjoint unions, of Loeb and selective metric spaces.

Countable Toronto spaces

Gary Gruenhage, J. Moore (2000)

Fundamenta Mathematicae

A space X is called an α-Toronto space if X is scattered of Cantor-Bendixson rank α and is homeomorphic to each of its subspaces of the same rank. We answer a question of Steprāns by constructing a countable α-Toronto space for each α ≤ ω. We also construct consistent examples of countable α-Toronto spaces for each α < ω 1 .

Countably metacompact spaces in the constructible universe

Paul Szeptycki (1993)

Fundamenta Mathematicae

We present a construction from ♢* of a first countable, regular, countably metacompact space with a closed discrete subspace that is not a G δ . In addition some nonperfect spaces with σ-disjoint bases are constructed.

Covering ω ω by special Cantor sets

Gary Gruenhage, Ronnie Levy (2002)

Commentationes Mathematicae Universitatis Carolinae

This paper deals with questions of how many compact subsets of certain kinds it takes to cover the space ω ω of irrationals, or certain of its subspaces. In particular, given f ∈ ω ( ω ∖ { 0 } ) , we consider compact sets of the form ∏ i ∈ ω B i , where | B i | = f ( i ) for all, or for infinitely many, i . We also consider “ n -splitting” compact sets, i.e., compact sets K such that for any f ∈ K and i ∈ ω , | { g ( i ) : g ∈ K , g ↾ i = f ↾ i } | = n .

Currently displaying 121 – 140 of 141