One point compactification for generalized quotient spaces

V. Karunakaran, C. Ganesan

Abstract

The concept of Generalized function spaces which were introduced and studied by Zemanian are further generalized as Boehmian spaces or as generalized quotient spaces in the recent literature. Their topological structure, notions of convergence in these space sare also investigated. Some sufficient conditions for the metrizability are also obtained. In this paper we shall assume that a generalized quotient space is non-compact and realize its one point compactification as a quotient space.

Keywords

Generalized quotient space; Compact; Locally compact and Hausdorff; One point compactification.

Full Text:

PDF

References

T. K. Boehme, The support of Mikusinski operators, Trans. Amer. Math. Soc. 176 (1973), 319–334.

V. Karunakaran and C. Ganesan, Topology and the notion of convergence on generalized quotient spaces, Int. J. Pure Appl. Math. 44, no. 5 (2008), 797–808.

J. Mikusinski and P. Mikusinski, Quotients de suites et leurs applications dans l’analyse fonctionnelle, Comptes Rendus 293, serie I (1981), 463–464.

J. Mikusinski and P. Mikusinski, Quotients of sequences, Proc. of the II conference on Convergence Szezyrk (1981), 39–45.

P. Mikusinski, Convergence of Boehmians, Japan J. Math 9 (1983), 159–179.

P. Mikusinski, Generalized quotients with applications in analysis, Methods Appl. Anal. 10 (2004), 377–386.

J. R. Munkres, Topology, second edition, Prentice-Hall of India, private limited, New Delhi (2003).

A. H. Zemanian, Generalized integral transformation, John Wiley and Sons, Inc., New York, (1968).

Abstract Views

1392
Metrics Loading ...

Metrics powered by PLOS ALM




Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt