On extension of the group operation over the Čech-Stone compactification

Jan Jełowicki

Displaying similar documents to “On extension of the group operation over the Čech-Stone compactification”

A little more on the product of two pseudocompact spaces

Eliza Wajch (1996)

Colloquium Mathematicae

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On sub-, pseudo- and quasimaximal spaces

J. Schröder (1998)

Commentationes Mathematicae Universitatis Carolinae

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The structure of sub-, pseudo- and quasimaximal spaces is investigated. A method of constructing non-trivial quasimaximal spaces is presented.

Tietze Extension Theorem for n-dimensional Spaces

Karol Pąk (2014)

Formalized Mathematics

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In this article we prove the Tietze extension theorem for an arbitrary convex compact subset of εn with a non-empty interior. This theorem states that, if T is a normal topological space, X is a closed subset of T, and A is a convex compact subset of εn with a non-empty interior, then a continuous function f : X → A can be extended to a continuous function g : T → εn. Additionally we show that a subset A is replaceable by an arbitrary subset of a topological space that is homeomorphic...

A contribution to the topological classification of the spaces Ср(X)

Robert Cauty, Tadeusz Dobrowolski, Witold Marciszewski (1993)

Fundamenta Mathematicae

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We prove that for each countably infinite, regular space X such that $C_{p} (X)$ is a $Z_{σ}$ -space, the topology of $C_{p} (X)$ is determined by the class $F_{0} (C_{p} (X))$ of spaces embeddable onto closed subsets of $C_{p} (X)$ . We show that $C_{p} (X)$ , whenever Borel, is of an exact multiplicative class; it is homeomorphic to the absorbing set $Ω_{α}$ for the multiplicative Borel class $M_{α}$ if $F_{0} (C_{p} (X)) = M_{α}$ . For each ordinal α ≥ 2, we provide an example $X_{α}$ such that $C_{p} (X_{α})$ is homeomorphic to $Ω_{α}$ .

Algebras of Borel measurable functions

Michał Morayne (1992)

Fundamenta Mathematicae

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We determine the size levels for any function on the hyperspace of an arc as follows. Assume Z is a continuum and consider the following three conditions: 1) Z is a planar AR; 2) cut points of Z have component number two; 3) any true cyclic element of Z contains at most two cut points of Z. Then any size level for an arc satisfies 1)-3) and conversely, if Z satisfies 1)-3), then Z is a diameter level for some arc.

On a problem of Steve Kalikow

Saharon Shelah (2000)

Fundamenta Mathematicae

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The Kalikow problem for a pair (λ,κ) of cardinal numbers,λ > κ (in particular κ = 2) is whether we can map the family of ω-sequences from λ to the family of ω-sequences from κ in a very continuous manner. Namely, we demand that for η,ν ∈ ω we have: η, ν are almost equal if and only if their images are. We show consistency of the negative answer, e.g., for $ℵ_{ω}$ but we prove it for smaller cardinals. We indicate a close connection with the free subset property and its variants. ...