Concerning web-like continua

John Walter Hinrichsen

Vol. 39 (1971), No. 3, 691–694

DOI: 10.2140/pjm.1971.39.691

Abstract

The compact metric continuum M is said to be a web if and only if there exist two monotone upper semi-continuous decompositions G₁ and G₂ of M such that M∕G₁ and M∕G₂ are arcs and each element of G₁ intersects each element of G₂. It is shown that there exists in Euclidean 3-space a compact continuum M that is not a web but does have two monotone upper semicontinuous decompositions G₁ and G₂ such that (1) M∕G₁ and M∕G₂ are simple closed curves and (2) each element of G₁ intersects each element of G₂. Such continua are called pseudo-webs.

Mathematical Subject Classification 2000

Primary: 54F15

Milestones

Received: 15 April 1970

Revised: 1 June 1971

Published: 1 December 1971