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Displaying 21 – 40 of 73

Reflecting character and pseudocharacter

Lucia R. Junqueira, Alberto M. E. Levi (2015)

Commentationes Mathematicae Universitatis Carolinae

We say that a cardinal function $φ$ reflects an infinite cardinal $κ$ , if given a topological space $X$ with $φ (X) \geq κ$ , there exists $Y \in {[X]}^{\leq κ}$ with $φ (Y) \geq κ$ . We investigate some problems, discussed by Hodel and Vaughan in Reflection theorems for cardinal functions, Topology Appl. 100 (2000), 47–66, and Juhász in Cardinal functions and reflection, Topology Atlas Preprint no. 445, 2000, related to the reflection for the cardinal functions character and pseudocharacter. Among other results, we present some new equivalences with...

Reflecting Lindelöf and converging ω₁-sequences

Alan Dow, Klaas Pieter Hart (2014)

Fundamenta Mathematicae

We deal with a conjectured dichotomy for compact Hausdorff spaces: each such space contains a non-trivial converging ω-sequence or a non-trivial converging ω₁-sequence. We establish that this dichotomy holds in a variety of models; these include the Cohen models, the random real models and any model obtained from a model of CH by an iteration of property K posets. In fact in these models every compact Hausdorff space without non-trivial converging ω₁-sequences is first-countable and, in addition,...

Reflective functors via nearness

S. Naimpally (1974)

Fundamenta Mathematicae

Reflexive families of closed sets

Zhongqiang Yang, Dongsheng Zhao (2006)

Fundamenta Mathematicae

Let S(X) denote the set of all closed subsets of a topological space X, and C(X) the set of all continuous mappings f:X → X. A family 𝓐 ⊆ S(X) is called reflexive if there exists ℱ ⊆ C(X) such that 𝓐 = {A ∈ S(X): f(A) ⊆ A for every f ∈ ℱ}. We investigate conditions ensuring that a family of closed subsets is reflexive.

Regular and Other Kinds of Extensions of Topological Spaces

Dimov, G. (1998)

Serdica Mathematical Journal

∗ This work was partially supported by the National Foundation for Scientific Researches at the Bulgarian Ministry of Education and Science under contract no. MM-427/94.In this paper the notion of SR-proximity is introduced and in virtue of it some new proximity-type descriptions of the ordered sets of all (up to equivalence) regular, resp. completely regular, resp. locally compact extensions of a topological space are obtained. New proofs of the Smirnov Compactification Theorem [31] and of the...

We study some relations whose compatibility with the topology is equivalent to normality or to complete regularity.

Currently displaying 21 – 40 of 73

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Displaying 21 – 40 of 73

Reflecting character and pseudocharacter

Reflecting Lindelöf and converging ω₁-sequences

Reflective functors via nearness

Reflexive families of closed sets

Regular and Other Kinds of Extensions of Topological Spaces

Regular fuzzy spaces and fuzzy almost regular spaces

Regular representations of semisimple MV-algebras by continuous real functions

Regular $ℒ$ -spaces

Regular spaces and relations

Regularity and extension of mappings in sequential spaces

Regularity and extension of maps

Regularity and normality on L-topological spaces. I.

Regularity and normality via ideals.

Regularity in convergence spaces

Regulated bases and completions of regular spaces

Regulated semilattices and locally compact spaces

Relaciones entre orden, normalidad y completa regularidad.

Relations between ß X / X and a Certain Subspace of ... X.

Relations between the $𝔑$ -completeness and the paracompactness of closure spaces

Relative compactness and recent common generalizations of metric and locally compact spaces

Currently displaying 21 – 40 of 73