For more information on the seminar, see: https://pgadey.ca/seminar/.

Abstract: In descriptive set theory, the spaces of greatest interest are Polish spaces. After reviewing some topology, we will begin by defining what a Polish space is and explore some of their key features. After this we will discuss some embedding results involving an incredibly important Polish space known as the Cantor space. Finally, we will discuss how these embedding results can be used to prove a duality between measure and category, which builds a bridge between the analytical and topological notions of small sets. No background in set theory (beyond naive set theory) will be assumed. A basic background in analysis will be assumed, and some basic topology would be an asset (though the background topology will be discussed as the need arises).
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