A theorem on continua

Volume 7 / 1925

R. Wilder Fundamenta Mathematicae 7 (1925), 311-313 DOI: 10.4064/fm-7-1-311-313

Abstract

The purpose of this paper is to prove Theoreme: Of two concentric circles C_1 and C_2, let C_1 be the smaller. Denote by H the point set which is the sum of C_1, C_2, and the annular domain bounded by C_1 and C_2. Let M be a continuum which contains a point A interior to C_1 and a point B exterior to C_2. If N is any connected subset of M containing A and B, N will contain at least one point of some continuum which is a subset of M and H, and which has at least one point in common with each of the circles C_1 and C_2.

Authors

  • R. Wilder

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