Some examples of nontaut subspaces

Satya Deo and Kalathoor Varadarajan

Vol. 147 (1991), No. 1, 47–56

DOI: 10.2140/pjm.1991.147.47

Abstract

We obtain a necessary and sufficient condition for the tautness of each closed subspace of a Hausdorff space X w.r.t. the Alexander-Spanier cohomology functor H^∘. This is used to give an example of a normal Hausdorff space on which the concepts of an L-theory and a continuous cohomology theory (as defined by Spanier) are not equivalent. Finally, we provide examples of non-taut subspaces with respect to the classical cohomology theories which possess some further curious properties.

Mathematical Subject Classification 2000

Primary: 55N20

Secondary: 55N30

Milestones

Received: 21 February 1989

Revised: 25 April 1989

Published: 1 January 1991