On a type of compactness via grills

Authors

  • B. Roy Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata–700019, INDIA Author
  • M. N. Mukherjee Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata–700019, INDIA Author

Keywords:

Grill, G-compactness, G-regularity, one-point compactification

Subjects:

54D35, 54D99

Abstract

In this paper, we introduce and study the idea of a new type ofcompactness, defined in terms of a grill G in atopological space X. Calling it G-compactness, weinvestigate its relation with compactness, among other things.Analogues of Alexender's subbase theorem and Tychonoff producttheorem are also obtained for G-compactness. Finally,we exhibit a new method, in terms of the deliberations here, forconstruction of the well known one-point compactification of aT2, locally compact and noncompact topological space.

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Published

2007-07-15