Weak continuity and almost continuity

Two relationships considered by Weston [1] for a pair of topologies on a set X are translated to a function setting. An attempt to characterize the two resulting types of functions leads to new characterizations of weak continuity and almost continuity. After showing that weak continuity and almost...

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Main Author:	D. A. Rose
Format:	Article
Language:	English
Published:	Hindawi Limited 1984-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Subjects:	weakly continuous function almost continuous function subweakly continuous function.
Online Access:	http://dx.doi.org/10.1155/S0161171284000338

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record_format	Article
spelling	doaj-74d0f6b2afe1421296d4782d485565302020-11-25T00:47:25ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-017231131810.1155/S0161171284000338Weak continuity and almost continuityD. A. Rose0Department of Mathematics, Francis Marion College, Florence, South Carolina 29501, USATwo relationships considered by Weston [1] for a pair of topologies on a set X are translated to a function setting. An attempt to characterize the two resulting types of functions leads to new characterizations of weak continuity and almost continuity. After showing that weak continuity and almost continuity are independent, interrelationships are sought. This leads to the definition of subweak continuity and a new characterization for almost openness. Finally, several published results are strengthened or slightly extended.http://dx.doi.org/10.1155/S0161171284000338weakly continuous functionalmost continuous functionsubweakly continuous function.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	D. A. Rose
spellingShingle	D. A. Rose Weak continuity and almost continuity International Journal of Mathematics and Mathematical Sciences weakly continuous function almost continuous function subweakly continuous function.
author_facet	D. A. Rose
author_sort	D. A. Rose
title	Weak continuity and almost continuity
title_short	Weak continuity and almost continuity
title_full	Weak continuity and almost continuity
title_fullStr	Weak continuity and almost continuity
title_full_unstemmed	Weak continuity and almost continuity
title_sort	weak continuity and almost continuity
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	1984-01-01
description	Two relationships considered by Weston [1] for a pair of topologies on a set X are translated to a function setting. An attempt to characterize the two resulting types of functions leads to new characterizations of weak continuity and almost continuity. After showing that weak continuity and almost continuity are independent, interrelationships are sought. This leads to the definition of subweak continuity and a new characterization for almost openness. Finally, several published results are strengthened or slightly extended.
topic	weakly continuous function almost continuous function subweakly continuous function.
url	http://dx.doi.org/10.1155/S0161171284000338
work_keys_str_mv	AT darose weakcontinuityandalmostcontinuity
_version_	1725260002880389120

Weak continuity and almost continuity

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