TITLE:
An Expository on Some Nonstandard Compactifications
AUTHORS:
Alagu Somasundaram, Rukhmoni Kala
KEYWORDS:
Non-Standard, Compactification, Completely Regular Space, Locally Compact Hausdorff Space, Locally Compact Abelian Group
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.11 No.10,
October
25,
2021
ABSTRACT: Three classical compactification procedures are presented with nonstandard flavour. This is to illustrate the applicability of Nonstandard analytic tool to beginners interested in Nonstandard analytic methods. The general procedure is as follows: A suitable equivalence relation is defined on an enlargement *X of the space X which is a completely regular space or a locally compact Hausdorff space or a locally compact Abelian group. Accordingly, every f in C(X,R) (the space of bounded continuous real valued functions on X) or Cc(X,R) (the space of continuous real valued functions on X with compact support) or the dual group Γof the locally compact Abelian group G is extended to the set of the above mentioned equivalence classes. A compact topology on is obtained as the weak topology generated by these extensions of f. Then X is naturally imbedded densely in .