COMPACTIFICATIONS OF A FIXED SET

Abstract

Compactification of a space X is a compact space containing X as a dense subspace. Magills construction for compactications of a fixed Tychonoff space through partitions is applied to derive compactications of various Tychonoff spaces (X;T), with a fixed set X and with a variation in Tychonoff topologies 'T'. Some possible extensions of mappings are obtained in this regard. Magills construction for compactications of a fixed Tychonoff space through partitions is applied to derive compactications of various Tychonoff spaces (X;T), with a fixed set X and with a variation in Tychonoff topologies 'T'. Some possible extensions of mappings are obtained in this regard. In a compact extension of a topological group, the inverse operation should be extendable homeomorphically from the base topological group. Finally mappings are extended homeomorphically from topological space to its compact extension, when topologies are also varied.