Extension of continuity of maps between axiomatic locally finite spaces

The paper studies the extension problem of continuous maps between axiomatic locally finite spaces (for short, ALF spaces). Indeed, an ALF space is a topological space satisfying a set of axioms suggested in . Further, an ALF space is defined by using a special kind of neighborhood different from th...

Full description

Bibliographic Details
Main Author:	Sangeon HAN
Format:	Article
Language:	zho
Published:	Hebei University of Science and Technology
Series:	Journal of Hebei University of Science and Technology
Subjects:	locally finite space axiomatic locally finite (ALF) space smallest open neighbourhood frontier neighbourhood relation homeomorphism local homeomorphism combinatorial homeomorphism abstract cell complex extension problem retract
Online Access:	http://xuebao.hebust.edu.cn/hbkjdx/ch/reader/create_pdf.aspx?file_no=b201501012&flag=1&journal_

id	doaj-5bb2a143f13b4e99bc6eb532fdca1999
record_format	Article
spelling	doaj-5bb2a143f13b4e99bc6eb532fdca19992020-11-24T22:49:39ZzhoHebei University of Science and TechnologyJournal of Hebei University of Science and Technology1008-1542361818910.7535/hbkd.2015yx01017b201501012Extension of continuity of maps between axiomatic locally finite spacesSangeon HAN0Department of Mathematics, Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju 561-756, KoreaThe paper studies the extension problem of continuous maps between axiomatic locally finite spaces (for short, ALF spaces). Indeed, an ALF space is a topological space satisfying a set of axioms suggested in . Further, an ALF space is defined by using a special kind of neighborhood different from the topological neighborhood in classical topology so that the continuity of maps between ALF spaces can be defined by preserving the neighborhood relation (see Definition 10). Therefore, it is necessary to develop the notions of continuity, homeomorphism and local homeomorphism for such spaces by using the neighborhood relation, which can be applicable in computer science. In the study of a deformation of an ALF space, we can develop a special kind of retract on ALF spaces. By using the retract, we can efficiently deal with the extension of continuous maps between ALF spaces.http://xuebao.hebust.edu.cn/hbkjdx/ch/reader/create_pdf.aspx?file_no=b201501012&flag=1&journal_locally finite spaceaxiomatic locally finite (ALF) spacesmallest open neighbourhoodfrontierneighbourhood relationhomeomorphismlocal homeomorphismcombinatorial homeomorphismabstract cell complexextension problemretract
collection	DOAJ
language	zho
format	Article
sources	DOAJ
author	Sangeon HAN
spellingShingle	Sangeon HAN Extension of continuity of maps between axiomatic locally finite spaces Journal of Hebei University of Science and Technology locally finite space axiomatic locally finite (ALF) space smallest open neighbourhood frontier neighbourhood relation homeomorphism local homeomorphism combinatorial homeomorphism abstract cell complex extension problem retract
author_facet	Sangeon HAN
author_sort	Sangeon HAN
title	Extension of continuity of maps between axiomatic locally finite spaces
title_short	Extension of continuity of maps between axiomatic locally finite spaces
title_full	Extension of continuity of maps between axiomatic locally finite spaces
title_fullStr	Extension of continuity of maps between axiomatic locally finite spaces
title_full_unstemmed	Extension of continuity of maps between axiomatic locally finite spaces
title_sort	extension of continuity of maps between axiomatic locally finite spaces
publisher	Hebei University of Science and Technology
series	Journal of Hebei University of Science and Technology
issn	1008-1542
description	The paper studies the extension problem of continuous maps between axiomatic locally finite spaces (for short, ALF spaces). Indeed, an ALF space is a topological space satisfying a set of axioms suggested in . Further, an ALF space is defined by using a special kind of neighborhood different from the topological neighborhood in classical topology so that the continuity of maps between ALF spaces can be defined by preserving the neighborhood relation (see Definition 10). Therefore, it is necessary to develop the notions of continuity, homeomorphism and local homeomorphism for such spaces by using the neighborhood relation, which can be applicable in computer science. In the study of a deformation of an ALF space, we can develop a special kind of retract on ALF spaces. By using the retract, we can efficiently deal with the extension of continuous maps between ALF spaces.
topic	locally finite space axiomatic locally finite (ALF) space smallest open neighbourhood frontier neighbourhood relation homeomorphism local homeomorphism combinatorial homeomorphism abstract cell complex extension problem retract
url	http://xuebao.hebust.edu.cn/hbkjdx/ch/reader/create_pdf.aspx?file_no=b201501012&flag=1&journal_
work_keys_str_mv	AT sangeonhan extensionofcontinuityofmapsbetweenaxiomaticlocallyfinitespaces
_version_	1725675469125189632

Extension of continuity of maps between axiomatic locally finite spaces

Similar Items