Studies on regular semi open sets In topological spaces

Abstract

The subject of topology is of interest in its own right lays the newlinefoundations for further study in analysis geometry and algebraic topology newlineThe basic and conventional division of topology is point set topology which newlinedescribes continuity homeomorphism of functions and the compactness and newlineconnectedness of topological spaces Topology can be defined as the newlinequalitative properties of certain objects called sets mappings functions and newlinetopological spaces newlineTopology is a bridge between geometry and algebra In recent years newlinemost of the new ideas in mathematics arose in topology from geometrical newlineimages and were then formalized and carried over to more algebraic fields In newlinetopology two geometrical objects are homeomorphic if the first can be newlinedeformed into the second by stretching and bending Cutting is also allowed newlinebut only if the two parts are later glued back together along exactly the same newlinecut For example a square and a circle are homeomorphic newlineThe traditional closed sets are extended to semi closed sets preclosed newlinesets generalized closed sets closed sets weakly closed sets newlinegeneralized weakly closed sets strongly g closed sets and the respective open newlinesets whose complement sets are associated closed sets newline newline