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Czasopisma help

  1. 4 Fundamenta Mathematicae

Autorzy help

  1. 2 Moore R. L.

  2. 2 Wilder R. L.

Lata help

  1. 3 1925

  2. 1 1924

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Concerning the common boundary of two domains

100%
Moore R. L.
Fundamenta Mathematicae
|
1924
|
tom 6
|
nr 1
203-213
EN
The main purpose of the present paper is to show that if a bounded continuum has more then one prime part and no one of its prime parts separates the plane then in order that it should have just two complementary domains and be the complete boundary of each of them it is necessary and sufficient that it should remain connected in the weak sense on the removal of any one of its connected proper subsets which is closed.
2
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A theorem on continua

100%
Wilder R. L.
Fundamenta Mathematicae
|
1925
|
tom 7
|
nr 1
311-313
EN
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.
3
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A characterisation of a continuous curve

88%
Moore R. L.
Fundamenta Mathematicae
|
1925
|
tom 7
|
nr 1
302-307
EN
The purpose of this paper is to prove: Théorème: In order that a continuum M should be a continuous curve it is necessary and sufficient that for every two distinct points A and B of M there should exist a subset of M which consists of a finite number of continua and which separates A from B in M. Théorème: In order that a bounded continuum M should be a continuous curve which contains no domain and does not separate the plane it is necessary and sufficient that for every two distinct points A and B which belong to M there should exist a point which separates A from B in M.
4
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Concerning continuous curves

88%
Wilder R. L.
Fundamenta Mathematicae
|
1925
|
tom 7
|
nr 1
340-377
EN
The present paper has three main objects: 1. to study the analogy between ordinary two-dimensional space and a plane continuous curve; 2. to characterize and analyze the boundaries of the domains complementary to a plane continuous curve; 3. to give a new characterization of continuous curves suitable for any number of dimensions;
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