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Axiom $T_{D}$ and the Simmons sublocale theorem

Jorge Picado, Aleš Pultr (2019)

Commentationes Mathematicae Universitatis Carolinae

More precisely, we are analyzing some of H. Simmons, S. B. Niefield and K. I. Rosenthal results concerning sublocales induced by subspaces. H. Simmons was concerned with the question when the coframe of sublocales is Boolean; he recognized the role of the axiom $T_{D}$ for the relation of certain degrees of scatteredness but did not emphasize its role in the relation between sublocales and subspaces. S. B. Niefield and K. I. Rosenthal just mention this axiom in a remark about Simmons’ result. In this...

Axioms weaker then $R_{0}$

J. Guia (1984)

Matematički Vesnik

Bemerkungen über TD-Räume.

Rudolf - E. Hoffmann (1974)

Manuscripta mathematica

Between closed sets and generalized closed sets in closure spaces

Chawalit Boonpok, Jeeranunt Khampakdee (2008)

Acta Mathematica Universitatis Ostraviensis

The purpose of the present paper is to define and study $\partial$ -closed sets in closure spaces obtained as generalization of the usual closed sets. We introduce the concepts of $\partial$ -continuous and $\partial$ -closed maps by using $\partial$ -closed sets and investigate some of their properties.

Bitopological hyperspaces equipped with upper semi-finite snd lower semi-finite topologies

R. Vasudevan, C. K. Goel (1981)

Matematički Vesnik

Cardinal invariants of paratopological groups

Iván Sánchez (2013)

Topological Algebra and its Applications

We show that a regular totally ω-narrow paratopological group G has countable index of regularity, i.e., for every neighborhood U of the identity e of G, we can find a neighborhood V of e and a countable family of neighborhoods of e in G such that ∩W∈γ VW−1⊆ U. We prove that every regular (Hausdorff) totally !-narrow paratopological group is completely regular (functionally Hausdorff). We show that the index of regularity of a regular paratopological group is less than or equal to the weak Lindelöf...