On the rim-structure of continuous images of ordered compacta

Jacek Nikiel, H. Murat Tuncali and Edward D. Tymchatyn

Vol. 149 (1991), No. 1, 145–155

DOI: 10.2140/pjm.1991.149.145

Abstract

Let X be a Hausdorff continuous image of an ordered continuum. Mardešić proved that X has a basis of open sets with metrizable boundaries. We use T-set approximations to obtain bases of open sets for X whose boundaries satisfy a variety of conditions. In particular, we prove that

dimX	= indX = IndX
	= max{1,sup{dimY : Y ⊂ X is metrizable and closed}}.

Mathematical Subject Classification 2000

Primary: 54F50

Secondary: 54E45, 54F45

Milestones

Received: 26 January 1990

Published: 1 May 1991