Characterizations of continua in which connected subsets are arcwise connected

Tymchatyn, E. D.

doi:10.1090/S0002-9947-1976-0423318-6

Characterizations of continua in which connected subsets are arcwise connected
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by E. D. Tymchatyn PDF

Trans. Amer. Math. Soc. 222 (1976), 377-388 Request permission

Abstract:

The purpose of this paper is to give several characterizations of the continua in which all connected subsets are arcwise connected. The methods used are those developed by B. Knaster and K. Kuratowski, G. T. Whyburn and the author. These methods depend on Bernstein’s decomposition of a topologically complete metric space into totally imperfect sets and on Whyburn’s theory of local cutpoints. Some properties of connected sets in finitely Suslinian spaces are obtained. Two questions raised by the author are answered. Several partial results of Whyburn are obtained as corollaries of the main result.

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On a problem of W. L. Ayres

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