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𝒯 0 - and 𝒯 1 -reflections

Maria Manuel Clementino (1992)

Commentationes Mathematicae Universitatis Carolinae

In an abstract category with suitable notions of subobject, closure and point, we discuss the separation axioms T 0 and T 1 . Each of the arising subcategories is reflective. We give an iterative construction of the reflectors and present characteristic examples.

-closed sets in biclosure spaces

Chawalit Boonpok (2009)

Acta Mathematica Universitatis Ostraviensis

In the present paper, we introduce and study the concept of -closed sets in biclosure spaces and investigate its behavior. We also introduce and study the concept of -continuous maps.

A Čech function in ZFC

Fred Galvin, Petr Simon (2007)

Fundamenta Mathematicae

A nontrivial surjective Čech closure function is constructed in ZFC.

A note on pseudobounded paratopological groups

Fucai Lin, Shou Lin, Iván Sánchez (2014)

Topological Algebra and its Applications

Let G be a paratopological group. Then G is said to be pseudobounded (resp. ω-pseudobounded) if for every neighbourhood V of the identity e in G, there exists a natural number n such that G = Vn (resp.we have G = ∪ n∈N Vn). We show that every feebly compact (2-pseudocompact) pseudobounded (ω-pseudobounded) premeager paratopological group is a topological group. Also,we prove that if G is a totally ω-pseudobounded paratopological group such that G is a Lusin space, then is G a topological group....

A note on weakly ( μ , λ ) -closed functions

Bishwambhar Roy (2013)

Mathematica Bohemica

In this paper we introduce a new class of functions called weakly ( μ , λ ) -closed functions with the help of generalized topology which was introduced by Á. Császár. Several characterizations and some basic properties of such functions are obtained. The connections between these functions and some other similar types of functions are given. Finally some comparisons between different weakly closed functions are discussed. This weakly ( μ , λ ) -closed functions enable us to facilitate the formulation of certain...

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