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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Two properties of $R^{N}$ with a compact group topology
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by Kevin J. Sharpe PDF
Proc. Amer. Math. Soc. 34 (1972), 267-269 Request permission

Abstract:

We let $R_c^N$ be a compact additive group, and we prove that if A is an $R_c^N$-measurable set, then one of the interiors of A and $A’$ in the usual topology for ${R^N}$ (written $R_u^N$) must be void. Also we show that the only functions from ${R^N}$ to a Hausdorff space that are both $R_u^N$-continuous and $R_c^N$-measurable are the constant functions.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 34 (1972), 267-269
  • MSC: Primary 22C05
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0293002-2
  • MathSciNet review: 0293002