The extendability of a continuous semi-metric on a Tychonoff space to a compactification of the space is discussed. The extended semi-metrics are continuous on compactifications, constructed through an axiomatic approach.
Some new concepts of semi-compact spaces and semi-compactifications are introduced. An axiomatic construction for all Hausdorff compactifications is extended to construct semi-compactifications.
A construction for all Hausdorff compactifications given in the article [2] is analysed further to obtain other topological extensions, namely, regular extensions and normal extensions. The method is also applied to derive and to study convex compactifications.
In this article, we deal with the soft separation axioms using soft points on soft topological space and discuss the characterizations and properties of them. We extend these separation axioms to the soft product of soft topological spaces. Also we provide correct examples for the wrong examples example:1, example:2 and example:3 given in article [8].
Disconnectedness in topological space is analyzed to obtain Hausdorff connectifications of that topological space. Hausdorff connectifications are obtained by some direct constructions and by some partitions of connectifications. Also lattice structure is included in the collection of all Hausdorff connectifications.2010 MSC: 54D35; 54D05; 54D40.
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