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Abstract:
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The aim of this thesis is to investigate several theorems concerning open and closed mappings of one topological space into another. Chapter I introduces the concept of open mappings and closed mappings. There necessary and sufficient conditions are given for a mapping to be l) closed and 2) open. Also some of the results of changing the strength of the topologies of the topological spaces being mapped are shown.
In the second chapter some of the characteristic properties of open and closed mappings on reparable metric topological spaces are shown. Also a necessary and sufficient condition for a closed mapping to be open is given. |