Browsing by Author "Kpeglo, Emmanuel Dodzi"

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    Weak and Weak Topologies
    (2005) Kpeglo, Emmanuel Dodzi
    The purpose of this project is to endow E with a smallest topology such that the maps фi,I Є I are continuous. We construct a topology r on E with minimum open sets which makes { фi }iЄI, continuous, where E is a non-empty set,{Yi}iЄI a family of topological spaces and, , continuous maps that take open seUts of E into open sets in Yi. фi: E → Yi Let ωi Є Yi. Therefore when ωi are open in Yi, i Є I, the set фi -1 (ωi) constitute a family of subsets of E which are necessarily open subsets in the topology τ; and we denote this family by U = {Ui}iЄI , where Ui = фi -1 (ωi) for some i Є I. The desired topology is constructed by finding the finite intersections of members of U and then arbitrary unions.