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2012•Basic Sciences Journal of Textile UniversitiesRequires access

Connectednesses of bi-pre-topological spaces

LI Sheng-gang, Shen Wen-xia

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Abstract

Connectednesses of bi-pre-topological spaces are studied by using topological and categorial methods.A characterization of connectednesses of bi-pre-topological spaces is given.It is proved that the category of bi-pre-topological spaces and continuous mappings between them is a topological construct,the smallest connectedness and the biggest connectedness of bi-pre-topological spaces exist,every connectedness of bi-pre-topological spaces is a continuously closed class,and the intersection of a family of connectednesses of bi-pre-topological spaces is still a connectednesses.Moreover,close connections between connectednesses of pre-topological spaces and connectednesses of bi-pre-topological spaces are established.

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What this paper is about

Connectednesses of bi-pre-topological spaces are studied by using topological and categorial methods.A characterization of connectednesses of bi-pre-topological spaces is given.It is proved that the category of bi-pre-topological spaces and continuous mappings between them is a topological construct,the smallest connectedness and the biggest connectedness of bi-pre-topological spaces exist,every connectedness of bi-pre-topological spaces is a continuously closed class,and the intersection of a family of connectednesses of bi-pre-topological spaces is still a connectednesses.Moreover,close connections between connectednesses of pre-topological spaces and connectednesses of bi-pre-topological spaces are established.

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Available abstract

Connectednesses of bi-pre-topological spaces are studied by using topological and categorial methods.A characterization of connectednesses of bi-pre-topological spaces is given.It is proved that the category of bi-pre-topological spaces and continuous mappings between them is a topological construct,the smallest connectedness and the biggest connectedness of bi-pre-topological spaces exist,every connectedness of bi-pre-topological spaces is a continuously closed class,and the intersection of a family of connectednesses of bi-pre-topological spaces is still a connectednesses.Moreover,close connections between connectednesses of pre-topological spaces and connectednesses of bi-pre-topological spaces are established.

Key concepts: Topological space, Topological tensor product, Topological vector space, Mathematics, Category of topological spaces, Separated sets, Social connectedness, Topology (electrical circuits)

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