


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 T_{1} spaces. This has several consequences, for example, in contrast with normality, monotone normality (when T_{1}axiom is a part of the definition) becomes an hereditary property. However, this is not the case when T_{1}axiom is not considered to be a part of the definition. In this talk we will study monotone normality in the absence of T_{1}axiom. In particular we will see which quasimetrizable 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: 
20110630

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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