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SPANS OF VARIOUS TWO CELLS, SURFACES, AND SIMPLE CLOSED CURVES
, 2002 T. T. West
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HOMOGENEITY DEGREE OF HYPERSPACES OF ARCS AND SIMPLE CLOSED CURVES
Rocky Mountain Journal of Mathematics, 2023A continuum is a compact connected nondegenerate metric space. By a hyperspace of a continuum \(X\) we mean a specified collection of subsets of \(X\) endowed with the Hausdorff metric. Given a continuum and integers \(n,m\) such that \(0\leq m
Rodrigo Hernández-Gutiérrez +1 more
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A Remarkable Simple Closed Curve
Annals of Mathematics, 1949Two simple closed curves in ordinary three dimensional space R are called equivalent' if there is an orientation-preserving homeomorphism of R on itself which transforms one curve into the other. A curve is called unknotted if it is equivalent to the circle X2 + y2 = 1, Z = 0, otherwise knotted. In a recent paper2 we have introduced the terms tame, for
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Simple-closed-curve sculptures of knots and links
Journal of Mathematics and the Arts, 2010We present a method for creating simple closed curves that divide the plane into two regions that, when coloured differently from one another, resemble knots and links. By cutting along these curves with a laser or water jet cutter, we obtain two-piece sculptures ideal for illustrating the Jordan curve theorem.
Robert Bosch
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Triangles inscribed in simple closed curves
Geometriae Dedicata, 1992Papers by \textit{M. D. Meyerson} [Fundam. Math. 110, 1-9 (1980; Zbl 0372.57003)] and \textit{E. H. Kronheimer} and \textit{P. B. Kronheimer} [J. Lond. Math. Soc., II. Ser. 24, 182-192 (1981; Zbl 0423.52001)] contain proofs that given any triangle \(T\) and any simple closed curve \(J\) there is a triangle similar to \(T\) having its vertices on \(J\) (
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MODELS AND HOMOGENEITY DEGREE OF HYPERSPACES OF A SIMPLE CLOSED CURVE
Rocky Mountain Journal of MathematicsA \textsl{continuum} is a nondegenerate, connected, compact, metric space. For a positive integer \(n\), \(C_n(X)\) is the hyperspace of all nonempty subsets of a continuum \(X\) having at most \(n\) components endowed with the Hausdorff metric, and \(F_n(X)\) is the closed subspace of \(C_n(X)\) consisting of all nonempty subsets of \(X\) having at ...
Alejandro Illanes
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Simple Closed Curves on Surraces
Bulletin of the London Mathematical Society, 1969The author announces an algorithm for determining whether a given element of the fundamental group \(\pi_1(M)\) of a connected compact 2-manifold \(M\) contains representatives which are simple closed curves. The algorithm is stated for the case \(M\) orientable, with or without boundary.
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Simple Arcs and Simple Closed Curves
1979A set homemorphic with a closed inverval is a simple arc. A set homemorphic with a circle of positive radius is a simple closed curve.
Gordon Whyburn, Edwin Duda
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On Unicoherency About a Simple Closed Curve
American Journal of Mathematics, 19331. The subject matter of this article is a discussion of a property of point-sets which is closely related to the properties of being connected and of being a unicoherent continuum, and is in a sense a generalization of both these properties. A unicoherent continuum is defined by Kuratowski t as one which cannot be expressed as the union of two ...
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Taming Wild Simple Closed Curves with Monotone Maps
Canadian Journal of Mathematics, 1972Hempel [6, Theorem 2] proved that if S is a tame 2-sphere in E3 and f is a map of E3 onto itself such that f|S is a homeomorphism and f(E3 - S) = E3- f(S), then f(S) is tame. Boyd [4] has shown that the converse is false; in fact,
Boyd, W. S., Wright, A. H.
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