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In this note we characterize the c-paracompact and c-collectionwise normal spaces in terms of continuous selections. We include the usual techniques with the required modifications by the cardinality.

Some continuous separation axioms

Phillip Zenor (1976)

Fundamenta Mathematicae

Some examples in the dimension theory of Tychonoff spaces

Elżbieta Pol (1979)

Fundamenta Mathematicae

Some examples related to colorings

Michael van Hartskamp, Jan van Mill (2000)

Commentationes Mathematicae Universitatis Carolinae

We complement the literature by proving that for a fixed-point free map $f : X \to X$ the statements (1) $f$ admits a finite functionally closed cover $𝒜$ with $f [A] \cap A = \emptyset$ for all $A \in 𝒜$ (i.e., a coloring) and (2) $β f$ is fixed-point free are equivalent. When functionally closed is weakened to closed, we show that normality is sufficient to prove equivalence, and give an example to show it cannot be omitted. We also show that a theorem due to van Mill is sharp: for every $n \geq 2$ we construct a strongly zero-dimensional Tychonov space...

Some factorization theorems for closed subspaces

W. Kulpa (1979)

Fundamenta Mathematicae

Some generalizations of completely normal spaces

S. P. Arya, M. P. Bhamini (1985)

Matematički Vesnik

Some more $κ$ -fully normal spaces

Hart, Klaas Pieter (1985)

Proceedings of the 13th Winter School on Abstract Analysis

Some Properties of the Sorgenfrey Line and the Sorgenfrey Plane

Adam St. Arnaud, Piotr Rudnicki (2013)

Formalized Mathematics

We first provide a modified version of the proof in [3] that the Sorgenfrey line is T1. Here, we prove that it is in fact T2, a stronger result. Next, we prove that all subspaces of ℝ1 (that is the real line with the usual topology) are Lindel¨of. We utilize this result in the proof that the Sorgenfrey line is Lindel¨of, which is based on the proof found in [8]. Next, we construct the Sorgenfrey plane, as the product topology of the Sorgenfrey line and itself. We prove that the Sorgenfrey plane...

Some remarks about bijections onto metric spaces

Alexander P. Shostak (1984)

Czechoslovak Mathematical Journal

Some results on expansions for normal and completely normal spaces.

Mary Powderly (1974)

Journal für die reine und angewandte Mathematik

Some topological consequences of the Product Measure Extension Axiom

Heikki Junnila (1983)

Fundamenta Mathematicae

Some topological properties weaker than Lindelofness

Yan-Kui Song (2008)

Matematički Vesnik

Spaces for which the diagonal has a closed neighborhood base

Klaas Pieter Hart (1987)

Colloquium Mathematicae

Spaces of continuous functions, $Σ$ -products and Box Topology

J. Angoa, Angel Tamariz-Mascarúa (2006)

Commentationes Mathematicae Universitatis Carolinae

For a Tychonoff space $X$ , we will denote by $X_{0}$ the set of its isolated points and $X_{1}$ will be equal to $X ∖ X_{0}$ . The symbol $C (X)$ denotes the space of real-valued continuous functions defined on $X$ . $□ ℝ^{κ}$ is the Cartesian product $ℝ^{κ}$ with its box topology, and $C_{□} (X)$ is $C (X)$ with the topology inherited from $□ ℝ^{X}$ . By $\hat{C} (X_{1})$ we denote the set ${f \in C (X_{1}) : f$ can be continuously extended to all of $X}$ . A space $X$ is almost- $ω$ -resolvable if it can be partitioned by a countable family of subsets in such a way that every non-empty open subset of $X$ has a non-empty...

Spaces with a binary normal subbase

van Mill, J. (1977)

Abstracta. 5th Winter School on Abstract Analysis

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