On the imbedding of subsets of a metric space in Jordan continua
R. Wilder (1932)
Fundamenta Mathematicae
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R. Wilder (1932)
Fundamenta Mathematicae
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R. Moore (1928)
Fundamenta Mathematicae
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Hakobyan, Hrant, Herron, David A. (2008)
Annales Academiae Scientiarum Fennicae. Mathematica
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R. Moore (1922)
Fundamenta Mathematicae
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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,...
R. Moore (1924)
Fundamenta Mathematicae
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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.
Khalimsky, Efim, Kopperman, Ralph, Meyer, Paul R. (1990)
Journal of Applied Mathematics and Stochastic Analysis
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L. A. Caffarelli, N. M. Rivière (1976)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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John Kline (1924)
Fundamenta Mathematicae
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The purpose of this paper is to prove: Theorem: Suppose M is a closed connected set containing more than one point such that if g is any connected subset of M, then M-g is connected. Under these conditions M is a simple closed curve. Theorem: If M is an unbounded closed connected set which remains connected upon the removal of any unbounded connected proper subset, then M is either an open curve, a ray of an open curve or a simple closed curve J plus OP, a ray of an open curve which...
Bernhard Schild (1986)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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