Journal Title

Transactions of the American Mathematical Society

Publication Date

8-1981

Abstract

A continuum is cyclicly connected provided each pair of its points lie together on some simple closed curve. In 1927, G. T. Whyburn proved that a locally connected plane continuum is cyclicly connected if and only if it contains no separating points. This theorem was fundamental in his original treatment of cyclic element theory. Since then numerous authors have obtained extensions of Whyburn's theorem. In this paper we characterize cyclic connectedness in the class of all Hausdorff continua.

Subjects

Continuum (Mathematics)

Publication Information

First published in Transactions of the American Mathematical Society, in 1981, published by the American Mathematical Society.

DOI

10.1090/S0002-9947-1981-0617540-5

Peer-Reviewed

Yes

Document Type

Journal Article

Included in

Mathematics Commons

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