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An answer to a question of Arhangel'skii

Henryk Michalewski (2001)

Commentationes Mathematicae Universitatis Carolinae

We prove that there exists an example of a metrizable non-discrete space X , such that C p ( X × ω ) ≈ l C p ( X ) but C p ( X × S ) ¬ ≈ l C p ( X ) where S = ( { 0 } ∪ { 1 n + 1 : n ∈ ω } ) and C p ( X ) is the space of all continuous functions from X into reals equipped with the topology of pointwise convergence. It answers a question of Arhangel’skii ([2, Problem 4]).

An answer to a question of Cao, Reilly and Xiong

Zafer Ercan, S. Onal (2006)

Czechoslovak Mathematical Journal

We present a simple proof of a Banach-Stone type Theorem. The method used in the proof also provides an answer to a conjecture of Cao, Reilly and Xiong.

An approach to covering dimensions

Miroslav Katětov (1995)

Commentationes Mathematicae Universitatis Carolinae

Using certain ideas connected with the entropy theory, several kinds of dimensions are introduced for arbitrary topological spaces. Their properties are examined, in particular, for normal spaces and quasi-discrete ones. One of the considered dimensions coincides, on these spaces, with the Čech-Lebesgue dimension and the height dimension of posets, respectively.

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