Displaying similar documents to “Almost closed sets and topologies they determine”

On AP and WAP spaces

Angelo Bella, Ivan V. Yashchenko (1999)

Commentationes Mathematicae Universitatis Carolinae

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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,...

A construction of a Fréchet-Urysohn space, and some convergence concepts

Aleksander V. Arhangel'skii (2010)

Commentationes Mathematicae Universitatis Carolinae

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Some strong versions of the Fréchet-Urysohn property are introduced and studied. We also strengthen the concept of countable tightness and generalize the notions of first-countability and countable base. A construction of a topological space is described which results, in particular, in a Tychonoff countable Fréchet-Urysohn space which is not first-countable at any point. It is shown that this space can be represented as the image of a countable metrizable space under a continuous pseudoopen...

Short proofs of two theorems in topology

Mohammad Ismail, Andrzej Szymański (1993)

Commentationes Mathematicae Universitatis Carolinae

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We present short and elementary proofs of the following two known theorems in General Topology: (i) [H. Wicke and J. Worrell] A T 1 weakly δ θ -refinable countably compact space is compact. (ii) [A. Ostaszewski] A compact Hausdorff space which is a countable union of metrizable spaces is sequential.