Some applications of minimal open sets

Some applications of minimal open sets

We characterize minimal open sets in topological spaces. We show that any nonempty subset of a minimal open set is pre-open. As an application of a theory of minimal open sets, we obtain a sufficient condition for a locally finite space to be a pre-Hausdorff space.

Bibliographic Details
Main Authors: Fumie Nakaoka, Nobuyuki Oda
Format: Article
Language:English
Published: Hindawi Limited 2001-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/S0161171201006482
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spelling doaj-24b4f54a10d64f668b5f155c8e1f11732020-11-24T23:21:55ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0127847147610.1155/S0161171201006482Some applications of minimal open setsFumie Nakaoka0Nobuyuki Oda1Department of Applied Mathematics, Fukuoka University, Nanakuma Jonan-ku, Fukuoka 814-0180, JapanDepartment of Applied Mathematics, Fukuoka University, Nanakuma Jonan-ku, Fukuoka 814-0180, JapanWe characterize minimal open sets in topological spaces. We show that any nonempty subset of a minimal open set is pre-open. As an application of a theory of minimal open sets, we obtain a sufficient condition for a locally finite space to be a pre-Hausdorff space.http://dx.doi.org/10.1155/S0161171201006482
collection DOAJ
language English
format Article
sources DOAJ
author Fumie Nakaoka
Nobuyuki Oda
spellingShingle Fumie Nakaoka
Nobuyuki Oda
Some applications of minimal open sets
International Journal of Mathematics and Mathematical Sciences
author_facet Fumie Nakaoka
Nobuyuki Oda
author_sort Fumie Nakaoka
title Some applications of minimal open sets
title_short Some applications of minimal open sets
title_full Some applications of minimal open sets
title_fullStr Some applications of minimal open sets
title_full_unstemmed Some applications of minimal open sets
title_sort some applications of minimal open sets
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2001-01-01
description We characterize minimal open sets in topological spaces. We show that any nonempty subset of a minimal open set is pre-open. As an application of a theory of minimal open sets, we obtain a sufficient condition for a locally finite space to be a pre-Hausdorff space.
url http://dx.doi.org/10.1155/S0161171201006482
work_keys_str_mv AT fumienakaoka someapplicationsofminimalopensets
AT nobuyukioda someapplicationsofminimalopensets
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