Displaying similar documents to “Concerning continuous curves”

Concerning the common boundary of two domains

R. Moore (1924)

Fundamenta Mathematicae

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The main purpose of the present paper is to show that if a bounded continuum has more then one prime part and no one of its prime parts separates the plane then in order that it should have just two complementary domains and be the complete boundary of each of them it is necessary and sufficient that it should remain connected in the weak sense on the removal of any one of its connected proper subsets which is closed.

Finite arc-sums

Norman Steenrod (1934)

Fundamenta Mathematicae

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On the generation of a simple surface by means of a set of equicontinuous curves

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...