A Construction for Semi-Compactifications

Ramkumar, S.; Moorthy, C. Ganesa

doi:10.1142/s1793557112500088

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2021

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“…The third section of this article is to study such extensions of mappings, when topologies are also varied. The authors have also contributed a classical work for compactifications including order relations (See: [11], [13], [14], [15]). Recent works are also available in literature regarding compactifications and lattice structure of a collection of compactifications (See: [2], [3], [7]).…”

Section: Introductionmentioning

confidence: 99%

Compactifications of a Fixed Set

Ramkumar¹

2021

Maltepe Journal of Mathematics

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If a Tychonoff space is fixed, then we may consider all possible Hausdorff compactifications of the space. If an infinite set is fixed, then we may vary Tychonoff topologies on the set and the compactifications may also be varied.Magills construction for compactifications of a fixed Tychonoff space through partitions is applied to derive compactifications of various Tychonoff spaces (X, τ ), with a fixed set X and with a variation in Tychonoff topologies τ . The structure of required partitions is also analyzed. When topologies are varied, some possible extensions of mappings are obtained in this regard.

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