Abstract

In this paper, we introduce and study the idea of a new type of compactness, defined in terms of a grill $\cal G$ in a topological space $X$. Calling it $\cal G$-compactness, we investigate its relation with compactness, among other things. Analogues of Alexender's subbase theorem and Tychonoff product theorem are also obtained for $\cal G$-compactness. Finally, we exhibit a new method, in terms of the deliberations here, for construction of the well known one-point compactification of a $T_2$, locally compact and noncompact topological space.

Keywords: Grill, $\cal G$-compactness, $\cal G$-regularity, one-point compactification.

MSC: 54D35, 54D99

Pages:  113$-$120     

Volume  59 ,  Issue  3 ,  2007