Displaying similar documents to “Boundaries in digital planes.”

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...

Continuity of the visibility function.

Ana Forte Cunto (1991)

Publicacions Matemàtiques

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G. Beer defined the visibility function of a set S and proved its continuity in the interior of S. It is proved here that the visibility function of a planar Jordan domain is continuous precisely at the cone points of the boundary of S.

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,...

Euclidean quasiconvexity.

Hakobyan, Hrant, Herron, David A. (2008)

Annales Academiae Scientiarum Fennicae. Mathematica

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The M-components of level sets of continuous functions in WBV.

Coloma Ballester, Vicent Caselles (2001)

Publicacions Matemàtiques

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We prove that the topographic map structure of upper semicontinuous functions, defined in terms of classical connected components of its level sets, and of functions of bounded variation (or a generalization, the WBV functions), defined in terms of M-connected components of its level sets, coincides when the function is a continuous function in WBV. Both function spaces are frequently used as models for images. Thus, if the domain Ω' of the image is Jordan domain, a rectangle, for instance,...