Continua of constant distances in span theory

Andrew Lelek

Vol. 123 (1986), No. 1, 161–171

DOI: 10.2140/pjm.1986.123.161

Abstract

It is proved that, for each non-negative number β not exceeding the span of a mapping f : X → Y , where X and Y are compact metric spaces, there exists a non-empty continuum K_β ⊂ X ×X with identical two projections and such that the distances between f(x) and f(x′) are all equal to β for (x,x′) ∈ K_β. Similar results hold for other types of spans.

Mathematical Subject Classification 2000

Primary: 54F15

Secondary: 54C05

Milestones

Received: 1 October 1984

Published: 1 May 1986