On Translations of Sets in Topological Groups
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Indian Institute of Advanced Study, Simla-5 ,IN
B. K. Lahiri
Abstract
Various authors {[5], [6], [7]} have obtained results on transformations of sets in the n-dimensional Euclidean space. In this paper, we prove some of these results in a topological group. In proving one of the results {Theorem 5.2}, we require a theorem on density of sets in a topological group which we prove with the help of a Vitali type theorem as proved in [1] for invariant measure. The theorem on density of sets {Theorem 5.1} has some interest in itself. The notion of density of sets has been extended from classical one [4] to a metric space [2] and to a measure space [8] and Romanovski space [10] with the help of a Vitali type theorem in a measure space [9].Downloads
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Copyright (c) 1975 B. K. Lahiri
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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