2007•Journal of MathematicsRequires access

r-CONNECTIVITY IN (WEAK) INDUCED TOPOLOGICAL SPACE

Shunqin Li

Abstract

The relationships between general topological space and its induced space, weak induced space and its base space are discussed; r-connectivity is defined by use of LF-r open set. It is obtained that a weak induced space is r-connected iff its base space is r-connected. These provide a convenient way for analysis of the structure of (weak) induced space.

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Key concepts: Space (punctuation), Mathematics, Base (topology), Connected space, Zero-dimensional space, Topology (electrical circuits), Topological space, Regular space