Department of

# Mathematics

Seminar Calendar
for events the day of Friday, August 10, 2018.

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Questions regarding events or the calendar should be directed to Tori Corkery.
      July 2018             August 2018           September 2018
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1  2  3  4  5  6  7             1  2  3  4                      1
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30


Friday, August 10, 2018

4:00 pm in Altgeld Hall,Friday, August 10, 2018

#### Definable topological spaces in o-minimal structures

###### Pablo Andujar Guerrero (Konstanz)

Abstract: In model theory a topological space can be interpreted naturally as a second order structure, namely a set and the unary relation of subsets that corresponds to the topology. A different approach is that of a first order structure in which there exists a topological space with a basis that is (uniformly) definable. We call this a definable topological space. A natural example corresponds to the order topology on any linearly ordered structure. During this talk I’ll present results on definable topological spaces in an o-minimal structure $\mathcal{R} = (R, ...)$. In particular we will classify Hausdorff definable topological spaces $(X, \tau )$ where $X \subseteq R$. We’ll consider a number of first order properties of these spaces that resemble topological properties and note how, in the o-minimal setting, the induced framework, which we might call “definable topology”, resembles general topology. This is joint work with Margaret Thomas and Erik Walsberg.