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g * -closed sets and a new separation axiom in Alexandroff spaces

Pratulananda Das, Md. Mamun Ar Rashid (2003)

Archivum Mathematicum

In this paper we introduce the concept of g * -closed sets and investigate some of its properties in the spaces considered by A. D. Alexandroff [1] where only countable unions of open sets are required to be open. We also introduce a new separation axiom called T w -axiom in the Alexandroff spaces with the help of g * -closed sets and investigate some of its consequences.

Hausdorff Fréchet closure spaces with maximum topological defect

Riccardo Ghiloni (2002)

Bollettino dell'Unione Matematica Italiana

It is well-known that the topological defect of every Fréchet closure space is less than or equal to the first uncountable ordinal number ω 1 . In the case of Hausdorff Fréchet closure spaces we obtain some general conditions sufficient so that the topological defect is exactly ω 1 . Some classical and recent results are deduced from our criterion.

Inserting measurable functions precisely

Javier Gutiérrez García, Tomasz Kubiak (2014)

Czechoslovak Mathematical Journal

A family of subsets of a set is called a σ -topology if it is closed under arbitrary countable unions and arbitrary finite intersections. A σ -topology is perfect if any its member (open set) is a countable union of complements of open sets. In this paper perfect σ -topologies are characterized in terms of inserting lower and upper measurable functions. This improves upon and extends a similar result concerning perfect topologies. Combining this characterization with a σ -topological version of Katětov-Tong...

Currently displaying 81 – 100 of 295