Authors
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B. K. Tyagi
Department of Mathematics, Atmaram Sanatan Dharma College, University of Delhi, New Delhi-110021, India
Author
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S. Luthra
Department of Mathematics, University of Delhi, New Delhi-110007, India
Author
Keywords:
Point-open topology, open-point topology, bi-point-open topology, topological group, zero dimensional, -narrow, disjoint shrinking, discrete selection
Subjects:
54C35, 54A10, 54C05, 54D10, 54D15, 54E35, 54H11
Abstract
In this paper, we study the notions of point-open topology , open-point topology and bi-point-open topology on , the set of all continuous functions from a topological space (topological group to a topological group . In this setting, we study the countability, separation axioms and metrizability. The equivalent conditions are given so that the space is a zero-dimensional topological group. Further, if is -regular, then is Hausdorff if and only if is discrete. It is shown that under certain conditions the topological groups , and are -narrow. Sufficient conditions are given for the topological spaces , and to be discretely selective and to have a disjoint shrinking.