Chains of simple closed curves and a dogbone space
E. Anderson (1971)
Fundamenta Mathematicae
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E. Anderson (1971)
Fundamenta Mathematicae
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Kaufmann, Ralph M., Livernet, Muriel, Penner, R. C. (2003)
Geometry & Topology
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Arnold R. Vobach (1968)
Czechoslovak Mathematical Journal
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D. Woodard (1929)
Fundamenta Mathematicae
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Goodman, Noah (2005)
Algebraic & Geometric Topology
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Lackenby, Marc (2002)
Geometry & Topology
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Jong Lee (1972)
Fundamenta Mathematicae
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R. Wilder (1925)
Fundamenta Mathematicae
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The present paper has three main objects: 1. to study the analogy between ordinary two-dimensional space and a plane continuous curve; 2. to characterize and analyze the boundaries of the domains complementary to a plane continuous curve; 3. to give a new characterization of continuous curves suitable for any number of dimensions;
Honda, Ko (2000)
Geometry & Topology
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Robert Moore (1923)
Fundamenta Mathematicae
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The purpose of this article is to prove: Theorem: Suppose that, in a given three dimensional space S, ABCD is a rectangle and G is a self-compact set of simple continuous arcs such that: 1. through each point of ABCD there is just one arc of G, 2. BC and AD are arcs of G, 3. no two arcs of G have a point in common, 4. each arc of G has one endpoint on the interval AB and one endpoint on the interval CD but contains no other point in common with either of these intervals, 5. the set of...