A strong form of the Phragmén-Brouwer theorem

Dickman, R. F.

doi:10.1090/S0002-9939-1984-0727261-4

A strong form of the Phragmén-Brouwer theorem
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Proc. Amer. Math. Soc. 90 (1984), 333-337 Request permission

Abstract:

In this paper we prove the following form of the Phragmen-Brouwer Theorem: a locally connected, connected normal ${T_1}$-space $X$ is unicoherent if and only if for every pair of disjoint nonseparating continua $C$ and $D$ in $X$, $C \cup D$ does not separate $X$. Among the several corollaries is the proposition: $X$ is multicoherent if and only if $X$ is the union of a circular chain of continua $\left \{ {{A_0},{A_1},{A_2},{A_3}} \right \}$ where no three of the ${A_i}$’s have a point in common.

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