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\begin{document}
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\huge{The Department of Mathematics}\\[0.1\baselineskip]
\Large{2020--21--A term}\\[0.2\baselineskip]
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\begin{description}
\item[Course Name]
O-minimality: topology without pathologies
\item[Course Number]
\LRE{201.1.6141}
\item[Course web page]\mbox{}\\
\url{https://www.math.bgu.ac.il//en/teaching/fall2021/courses/o-minimality}
\item[Lecturer]
Prof. Assaf Hasson,
\nolinkurl{},
Office 204
\item[Office Hours]
\url{https://www.math.bgu.ac.il/en/teaching/hours}
\end{description}
\section*{Abstract}
\section*{Requirements and grading\footnote{Information may change during the first two weeks of the term. Please consult the webpage for updates}}
\section*{Course topics}
In the 1980s A. Grothendieck suggest a project for developing a tame topology that will not suffer from the many counter-examples and pathologies known in classical topology. Nowadays many view the notion of o-minimality as successful fulfillment of this program: in o-minimal fields all (unary) functions are piecewise differentiable (and therefore infinitely differentiable at almost every point); unary functions are piecewise monotone, connectedness is the same as path connectedness and the axiom of choice holds for definable sets. In the o-minimal setting most of the classical differential calculus can be developed, and so are large portion of the theory of Lie groups, algebraic topology and much more. O-minimality plays a key role in real geometry and in recent years had a crucial role in important breakthroughs in Diophantine geometry and in Hodge theory.
In the course we will define o-minimality and develop its basic theory. We will show that real closed fields are o-minimal and discuss -- time permitting -- some applications.
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