Displaying similar documents to “The Steiner problem for infinitely many points”

Closed connected sets which remain connected upon the removal of certain, connected subsets

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...

Concerning connectedness im kleinen and a related property

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,...

Locally connected exceptional minimal sets of surface homeomorphisms

Andrzej Biś, Hiromichi Nakayama, Pawel Walczak (2004)

Annales de l’institut Fourier

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We deal with locally connected exceptional minimal sets of surface homeomorphisms. If the surface is different from the torus, such a minimal set is either finite or a finite disjoint union of simple closed curves. On the torus, such a set can admit also a structure similar to that of the Sierpiński curve.