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On monotone normality and subfitness
 
 
Description:  The notion of monotone normality was introduced in 1973 by Heath, Lutzer and Zenor as a strengthening of normality and is probably what you would guess if asked to define "normal in a monotone way". Every metrizable space and every linearly ordered space is monotonically normal. In fact, it could be argued that whenever a space can be "explicitly" and "constructively" shown to be normal, then it is probably monotonically normal.
From that pioneering paper there has been an extensive literature on the topic. However, with a few exceptions, monotonically normal spaces have always been considered to be T1 spaces. This has several consequences, for example, in contrast with normality, monotone normality (when T1-axiom is a part of the definition) becomes an hereditary property. However, this is not the case when T1-axiom is not considered to be a part of the definition.
In this talk we will study monotone normality in the absence of T1-axiom. In particular we will see which quasi-metrizable spaces are monotonically normal. We will also study the role of subfitness in this context. Finally we will present some related results in the context of Pointfree Topology.
Date:  2011-06-30
Start Time:   15:30
Speaker:  Javier Gutiérrez García (Univ. Basque Country, Bilbao, Spain)
Institution:  U. of the Basque Country
Research Groups: -Algebra, Logic and Topology
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