Short proofs of two theorems in topology

Mohammad Ismail; Andrzej Szymański

Displaying similar documents to “Short proofs of two theorems in topology”

A countably compact, separable space which is not absolutely countably compact

Jerry E. Vaughan (1995)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We construct a space having the properties in the title, and with the same technique, a countably compact $T_{2}$ topological group which is not absolutely countably compact.

Absolute countable compactness of products and topological groups

Yan-Kui Song (1999)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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)].

On AP and WAP spaces

Angelo Bella, Ivan V. Yashchenko (1999)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Several remarks on the properties of approximation by points (AP) and weak approximation by points (WAP) are presented. We look in particular at their behavior in product and at their relationships with radiality, pseudoradiality and related concepts. For instance, relevant facts are: (a) There is in ZFC a product of a countable WAP space with a convergent sequence which fails to be WAP. (b) $C_{p}$ over $σ$ -compact space is AP. Therefore AP does not imply even pseudoradiality in function spaces,...