Monotone normality in products

Abstract

Monotone normality in finite and infinite topological products is investigated. As shown in (Heath et al., 1973), the countable (Tychonoff) power of a space is monotonically normal if and only if the space is stratifiable. It is shown that if the square of a space is monotonically normal, then all finite powers are monotonically normal and hereditarily paracompact. For certain special cases, it is observed that a space has all finite powers monotonically normal if and only if it linearly stratifiable. Nonetheless, a monotonically normal topological group is constructed, all of whose finite powers are monotonically normal, but which is not linearly stratifiable. The group is constructed using special filters and nonstandard topologies on infinite products.Copyright 1999 Elsevier B.V. All rights reserved. Re-use of this article is permitted in accordance with the Terms and Conditions set out at http://www.elsevier.com/open-access/userlicense/1.0