Vol. 36, No. 2, 1971

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An n-arc theorem for Peano spaces

J. H. V. Hunt

Vol. 36 (1971), No. 2, 351–356
Abstract

G. T. Whyburn gave an elementary inductive proof of the n-arc theorem for Peano spaces, which had originally been proved by G. Nobeling and K. Menger. In the course of doing this he gave a necessary and sufficient condition for there to be n disjoint arcs joining two disjoint closed sets A and B in a Peano space S. In this paper we split the set A into n disjoint closed subsets A1,A2,,An and give a necessary and sufficient condition for there to be n disjoint arcs joining A1 A2 An and B in S, exactly one arc meeting each Ai. Our proof uses the inductive technique that Whyburn introduced.

Mathematical Subject Classification
Primary: 54.55
Milestones
Received: 26 August 1970
Published: 1 February 1971
Authors
J. H. V. Hunt