Approach Merotopological Spaces and their Completion

Approach Merotopological Spaces and their Completion

This paper introduces the concept of an approach merotopological space and studies its category-theoretic properties. Various topological categories are shown to be embedded into the category whose objects are approach merotopological spaces. The order structure of the family of all approach merotop...

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Main Authors: Mona Khare, Surabhi Tiwari
Format: Article
Language:English
Published: Hindawi Limited 2010-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2010/409804
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spelling doaj-37e8a4d6882f45758302c6bd5494b2732020-11-24T22:45:56ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252010-01-01201010.1155/2010/409804409804Approach Merotopological Spaces and their CompletionMona Khare0Surabhi Tiwari1Department of Mathematics, University of Allahabad, Allahabad 211002, IndiaDepartment of Mathematics, University of Allahabad, Allahabad 211002, IndiaThis paper introduces the concept of an approach merotopological space and studies its category-theoretic properties. Various topological categories are shown to be embedded into the category whose objects are approach merotopological spaces. The order structure of the family of all approach merotopologies on a nonempty set is discussed. Employing the theory of bunches, bunch completion of an approach merotopological space is constructed. The present study is a unified look at the completion of metric spaces, approach spaces, nearness spaces, merotopological spaces, and approach merotopological spaces.http://dx.doi.org/10.1155/2010/409804
collection DOAJ
language English
format Article
sources DOAJ
author Mona Khare
Surabhi Tiwari
spellingShingle Mona Khare
Surabhi Tiwari
Approach Merotopological Spaces and their Completion
International Journal of Mathematics and Mathematical Sciences
author_facet Mona Khare
Surabhi Tiwari
author_sort Mona Khare
title Approach Merotopological Spaces and their Completion
title_short Approach Merotopological Spaces and their Completion
title_full Approach Merotopological Spaces and their Completion
title_fullStr Approach Merotopological Spaces and their Completion
title_full_unstemmed Approach Merotopological Spaces and their Completion
title_sort approach merotopological spaces and their completion
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2010-01-01
description This paper introduces the concept of an approach merotopological space and studies its category-theoretic properties. Various topological categories are shown to be embedded into the category whose objects are approach merotopological spaces. The order structure of the family of all approach merotopologies on a nonempty set is discussed. Employing the theory of bunches, bunch completion of an approach merotopological space is constructed. The present study is a unified look at the completion of metric spaces, approach spaces, nearness spaces, merotopological spaces, and approach merotopological spaces.
url http://dx.doi.org/10.1155/2010/409804
work_keys_str_mv AT monakhare approachmerotopologicalspacesandtheircompletion
AT surabhitiwari approachmerotopologicalspacesandtheircompletion
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