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1
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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 characterisation of a continuous curve

100%
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.
3
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Concerning connectedness im kleinen and a related property

100%
Moore R. L.
Fundamenta Mathematicae
|
1922
|
tom 3
|
nr 1
232-237
EN
Sierpinski has shown (Wacław Sierpiński Sur une condition pour qu'un continu soit une courbe jordanienne, Fundamenta Mathematicae I (1920), pp. 44-60) that in order that a closed and connected set of points M should be a continuous curve it is necessary and sufficient that, for every positive number ϵ, the connected point-set M should be the sum of a finite number of closed and connected point-sets each of diameter less than ϵ. It follows that, as applied to point-sets which are closed, bounded and connected, this property is equivalent to that of connectedness "im kleinen". The purpose of the present paper is to make a further study of these two properties (or rather suitable modifications of these properties) especially as applied to sets which are not necessarily closed.
4
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Concerning the relation between separability and the proposition that every uncountable point set has a limit point

100%
Moore R. L.
Fundamenta Mathematicae
|
1926
|
tom 8
|
nr 1
189-192
EN
The purpose of this paper is to establish two theorems: Theoreme: In order that every subclass of a given class D of Fréchet should be separable it is necessary and sufficient that every uncountable subclass of that class D should have a limit point. Theoreme: If D_s is a separable class D then every uncountable subclass of D_s contains a point of condensation.
5
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Concerning the sum of a countable number of mutually exclusive continua in the plane

100%
Moore R. L.
Fundamenta Mathematicae
|
1924
|
tom 6
|
nr 1
189-202
FR
In 1918 Sierpiński showed that if the sum of a countably infinite collection of closed point sets is bounded then it is not a continuum. He raised the question weather this theorem remains true if the restriction that the sum should be bounded is removed from the hypothesis. The purpose of the present paper is to show that for the case where each point set of the collection in question is itself a continuum, this question may be answered in the affirmative.
6
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Concerning triodic continua in the plane

32%
Moore R. L.
Fundamenta Mathematicae
|
1929
|
tom 13
|
nr 1
261-263
7
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A set of axioms for plane analysis situs

32%
Moore R. L.
Fundamenta Mathematicae
|
1935
|
tom 25
|
nr 1
13-28
8
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A separation theorem

26%
Moore R. L.
Fundamenta Mathematicae
|
1928
|
tom 12
|
nr 1
295-297
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