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A note on splittable spaces

Vladimir Vladimirovich Tkachuk (1992)

Commentationes Mathematicae Universitatis Carolinae

A space X is splittable over a space Y (or splits over Y ) if for every A X there exists a continuous map f : X Y with f - 1 f A = A . We prove that any n -dimensional polyhedron splits over 𝐑 2 n but not necessarily over 𝐑 2 n - 2 . It is established that if a metrizable compact X splits over 𝐑 n , then dim X n . An example of n -dimensional compact space which does not split over 𝐑 2 n is given.

A note on topological groups and their remainders

Liang-Xue Peng, Yu-Feng He (2012)

Czechoslovak Mathematical Journal

In this note we first give a summary that on property of a remainder of a non-locally compact topological group G in a compactification b G makes the remainder and the topological group G all separable and metrizable. If a non-locally compact topological group G has a compactification b G such that the remainder b G G of G belongs to 𝒫 , then G and b G G are separable and metrizable, where 𝒫 is a class of spaces which satisfies the following conditions: (1) if X 𝒫 , then every compact subset of the space X is a...

A remark on the tightness of products

Oleg Okunev (1996)

Commentationes Mathematicae Universitatis Carolinae

We observe the existence of a σ -compact, separable topological group G and a countable topological group H such that the tightness of G is countable, but the tightness of G × H is equal to 𝔠 .

A sufficient condition for maximal resolvability of topological spaces

Jerzy Bienias, Małgorzata Terepeta (2004)

Commentationes Mathematicae Universitatis Carolinae

We show a new theorem which is a sufficient condition for maximal resolvability of a topological space. We also discuss some relationships between various theorems about maximal resolvability.

AB-compacta

Isaac Gorelic, István Juhász (2008)

Commentationes Mathematicae Universitatis Carolinae

About remainders in compactifications of homogeneous spaces

D. Basile, Angelo Bella (2009)

Commentationes Mathematicae Universitatis Carolinae

We prove a dichotomy theorem for remainders in compactifications of homogeneous spaces: given a homogeneous space X , every remainder of X is either realcompact and meager or Baire. In addition we show that two other recent dichotomy theorems for remainders of topological groups due to Arhangel’skii cannot be extended to homogeneous spaces.

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