Some Additional Properties of Monotonically T₂ and m_i-spaces
by
Robert E. Buck
Slippery Rock University

Ito showed that stratifiable spaces in which there is a closure preserving local base at each point are M₁. That local version of M₁ is called m₁, while m₂ and m₃ are analogously defined. We look at some of the properties of these spaces. Monotone normality can also be generalized to monotonically T₂:

There is a function g assigning to each ordered pair (x, y) of distinct points in X a neighborhood, g(x, y), of x such that g(x, y) ∩g(y, x) = ∅ and

x ∈ È {g(x, y) | y ∈ M}   ⇒ x ∈ M

The monotone T₂ property has some advantages over monotone normality. We show, for example, that it is preserved under arbitrary box products. We examine some other situations where it is (or is not) preserved. We also discuss the surprisingly strong relationship between the m_i-spaces and the monotone T₂ property.

Date received: April 12, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caae-09.