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A solution to Comfort's question on the countable compactness of powers of a topological group

Artur Hideyuki Tomita (2005)

Fundamenta Mathematicae

In 1990, Comfort asked Question 477 in the survey book “Open Problems in Topology”: Is there, for every (not necessarily infinite) cardinal number $α \leq 2^{}$ , a topological group G such that $G^{γ}$ is countably compact for all cardinals γ < α, but $G^{α}$ is not countably compact? Hart and van Mill showed in 1991 that α = 2 answers this question affirmatively under $M A_{c o u n t a b l e}$ . Recently, Tomita showed that every finite cardinal answers Comfort’s question in the affirmative, also from $M A_{c o u n t a b l e}$ . However, the question has remained...

A unique factorization theorem for countable products of circles

Carl Eberhart (1967)

Fundamenta Mathematicae

Absolute countable compactness of products and topological groups

Yan-Kui Song (1999)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we generalize Vaughan's and Bonanzinga's results on absolute countable compactness of product spaces and give an example of a separable, countably compact, topological group which is not absolutely countably compact. The example answers questions of Matveev [8, Question 1] and Vaughan [9, Question (1)].

Displaying 21 – 27 of 27

A solution to Comfort's question on the countable compactness of powers of a topological group

A unique factorization theorem for countable products of circles

Absolute countable compactness of products and topological groups

Amorphe Potenzen kompakter Räume.

An application of the theory of isosceles (ultrametric) spaces to the Trnková-Vinárek theorem

An elementary proof of Noble's theorem on normality of powers

Aronszajn orderings.

Currently displaying 21 – 27 of 27