# A theorem on continua

Fundamenta Mathematicae (1925)

• Volume: 7, Issue: 1, page 311-313
• ISSN: 0016-2736

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## Abstract

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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.

## How to cite

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Wilder, R.. "A theorem on continua." Fundamenta Mathematicae 7.1 (1925): 311-313. <http://eudml.org/doc/214583>.

@article{Wilder1925,
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.},
author = {Wilder, R.},
journal = {Fundamenta Mathematicae},
keywords = {zbiór domknięty; zbiór spójny; krzywa ciągła; continuum},
language = {eng},
number = {1},
pages = {311-313},
title = {A theorem on continua},
url = {http://eudml.org/doc/214583},
volume = {7},
year = {1925},
}

TY - JOUR
AU - Wilder, R.
TI - A theorem on continua
JO - Fundamenta Mathematicae
PY - 1925
VL - 7
IS - 1
SP - 311
EP - 313
AB - 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.
LA - eng
KW - zbiór domknięty; zbiór spójny; krzywa ciągła; continuum
UR - http://eudml.org/doc/214583
ER -

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