Conditions which ensure that a simple map does not raise dimension
W. Dębski,J. Mioduszewski +1 more
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This article is published in Colloquium Mathematicum.The article was published on 1992-01-01 and is currently open access. It has received 2 citations till now. The article focuses on the topics: Dendrite (mathematics).read more
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Exactly k-to-1 maps: from pathological functions with finitely many discontinuities to well-behaved covering maps
TL;DR: In this paper, a survey of k-to-1 maps from one metric continuum to another is presented, with new results, old results and ideas for further research and a baker's dozen of questions are raised.
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Compositions of simple maps
TL;DR: In this paper, it was proved that every closed map of order k defined on an n-dimensional metric space is a composition of (n + 1)k 1 simple closed maps with metric domains.
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A plane continuum no two of whose nondegenerate subcontinua are homeomorphic: An application of inverse limits
R. D. Anderson,Gustave Choquet +1 more
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A chainable continuum no two of whose nondegenerate subcontinua are homeomorphic
TL;DR: In this article, Borsuk and Reichbach give a generalization of the fundamental theorem of algebra, Bull. Acad. Math, vol. 7 (1958) pp. 155-164.
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Über die Abbildung einer Strecke auf ein Quadrat
TL;DR: In this article, Gantor et al. showed that for every stetigen Abbildung einer Strecke auf ein Quadrat diejenigen Punkte des Quadrates, denen mindestens zwei Punkte der strecke entsprechen, eine Menge von der Mochtigkeit des Kontinuums bilden, and dass es eine im Quadrate uberall dichthegende Menge of Punkten gibt.