One point compactification for generalized quotient spaces

V. Karunakaran; C. Ganesan

doi:10.4995/agt.2010.1725

Authors

V. Karunakaran Madurai Kamaraj University
C. Ganesan Madurai Kamaraj University

DOI:

https://doi.org/10.4995/agt.2010.1725

Keywords:

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

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.

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Author Biographies

V. Karunakaran, Madurai Kamaraj University

Senior Professor, School of Mathematics, Madurai Kamaraj University, Tamil Nadu, Madurai - 625 021, India.

C. Ganesan, Madurai Kamaraj University

Research Scholar, School of Mathematics, Madurai Kamaraj University, Tami lNadu, Madurai - 625 021, India.

References

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