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A convergence on Boolean algebras generalizing the convergence on the Aleksandrov cube

Miloš S. Kurilić, Aleksandar Pavlović (2014)

Czechoslovak Mathematical Journal

We compare the forcing-related properties of a complete Boolean algebra 𝔹 with the properties of the convergences λ s (the algebraic convergence) and λ ls on 𝔹 generalizing the convergence on the Cantor and Aleksandrov cube, respectively. In particular, we show that λ ls is a topological convergence iff forcing by 𝔹 does not produce new reals and that λ ls is weakly topological if 𝔹 satisfies condition ( ) (implied by the 𝔱 -cc). On the other hand, if λ ls is a weakly topological convergence, then 𝔹 is a 2 𝔥 -cc algebra...

A note on g -metrizable spaces

Jinjin Li (2003)

Czechoslovak Mathematical Journal

In this paper, the relationships between metric spaces and g -metrizable spaces are established in terms of certain quotient mappings, which is an answer to Alexandroff’s problems.

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)].

Almost closed sets and topologies they determine

Vladimir Vladimirovich Tkachuk, Ivan V. Yashchenko (2001)

Commentationes Mathematicae Universitatis Carolinae

We prove that every countably compact AP-space is Fréchet-Urysohn. It is also established that if X is a paracompact space and C p ( X ) is AP, then X is a Hurewicz space. We show that every scattered space is WAP and give an example of a hereditarily WAP-space which is not an AP-space.

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