Vol. 82, No. 2, 1979

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A common fixed point theorem for nested spaces

Raymond Earl Smithson

Vol. 82 (1979), No. 2, 533–537
Abstract

Let X be an arcwise connected Hausdorff space in which the union of any nest of arcs is contained in an arc. Let f,g : X X be commuting functions (not necessarily continuous), which satisfy (1) f(A) and g(A) are arcwise connected for each arc A X, and (2) f1(x) and g1(x) are arcwise connected for each x X. The principal result of this paper is:

Theorem. The functions f and g have a common fixed point.

Mathematical Subject Classification 2000
Primary: 54H25
Milestones
Received: 14 July 1978
Revised: 15 February 1979
Published: 1 June 1979
Authors
Raymond Earl Smithson