On the argument functions of simple closed curves and simple arcs
E. R. Van Kampen (1937)
Compositio Mathematica
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E. R. Van Kampen (1937)
Compositio Mathematica
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Hugo Steinhaus (1954)
Colloquium Mathematicum
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J. Roberts (1932)
Fundamenta Mathematicae
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Lucille Whyburn (1937)
Fundamenta Mathematicae
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Karol Borsuk (1947)
Fundamenta Mathematicae
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Marston Morse, J. Jenkins (1952)
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;
H. Eggleston (1955)
Fundamenta Mathematicae
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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...
D. Bourgin (1959)
Fundamenta Mathematicae
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