Almost-continuous path connected spaces

M. K. Singal and Asha Rani Singal have defined an almost-continuous function f:X→Y to be one in which for each x∈X and each regular-open set V containing f(x), there exists an open U containing x such that f(U)⊂V. A space Y may now be defined to be almost-continuous path connected if for each y0,y1∈...

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Bibliographic Details
Main Authors:	Larry L. Herrington, Paul E. Long
Format:	Article
Language:	English
Published:	Hindawi Limited 1981-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Subjects:	almost-continuous functions path connected spaces.
Online Access:	http://dx.doi.org/10.1155/S0161171281000641

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spelling	doaj-a1775541cade49e881760206724468bc2020-11-24T22:36:41ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251981-01-014482382510.1155/S0161171281000641Almost-continuous path connected spacesLarry L. Herrington0Paul E. Long1Department of Mathematics, Louisiana State University at Alexandria, Alexandria, Louisiana 71402, USADepartment of Mathematics, The University of Arkansas at Fayetteville, Fayetteville, Arkansas 72701, USAM. K. Singal and Asha Rani Singal have defined an almost-continuous function f:X→Y to be one in which for each x∈X and each regular-open set V containing f(x), there exists an open U containing x such that f(U)⊂V. A space Y may now be defined to be almost-continuous path connected if for each y0,y1∈Y there exists an almost-continuous f:I→Y such that f(0)=y0 and f(1)=y1 An investigation of these spaces is made culminating in a theorem showing when the almost-continuous path connected components coincide with the usual components of Y.http://dx.doi.org/10.1155/S0161171281000641almost-continuous functionspath connected spaces.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Larry L. Herrington Paul E. Long
spellingShingle	Larry L. Herrington Paul E. Long Almost-continuous path connected spaces International Journal of Mathematics and Mathematical Sciences almost-continuous functions path connected spaces.
author_facet	Larry L. Herrington Paul E. Long
author_sort	Larry L. Herrington
title	Almost-continuous path connected spaces
title_short	Almost-continuous path connected spaces
title_full	Almost-continuous path connected spaces
title_fullStr	Almost-continuous path connected spaces
title_full_unstemmed	Almost-continuous path connected spaces
title_sort	almost-continuous path connected spaces
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	1981-01-01
description	M. K. Singal and Asha Rani Singal have defined an almost-continuous function f:X→Y to be one in which for each x∈X and each regular-open set V containing f(x), there exists an open U containing x such that f(U)⊂V. A space Y may now be defined to be almost-continuous path connected if for each y0,y1∈Y there exists an almost-continuous f:I→Y such that f(0)=y0 and f(1)=y1 An investigation of these spaces is made culminating in a theorem showing when the almost-continuous path connected components coincide with the usual components of Y.
topic	almost-continuous functions path connected spaces.
url	http://dx.doi.org/10.1155/S0161171281000641
work_keys_str_mv	AT larrylherrington almostcontinuouspathconnectedspaces AT paulelong almostcontinuouspathconnectedspaces
_version_	1725718751711592448

Almost-continuous path connected spaces

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