Web page of Dmytro Savchuk
Topology is the study of shapes and spaces (literally, `study of a place'), and could be described as qualitative geometry. It concerns essential features that are unchanged on stretching or bending a space. It is a very wide-ranging and important field, and one of the fundamental areas of mathematics.
The course will begin with what is known as point-set topology. We will introduce the notion of a topological space, but we will mostly restrict our attention to the easier setting of subspaces of Euclidean space. We will give an assortment of examples, and discuss properties a space may enjoy such as connectedness and compactness. We will then (hopefully quickly) venture into basic algebraic topology, where topics include the classification of surfaces (such as the Klein bottle and the Mobius band, a surface with boundary), the fundamental group, covering spaces, and fixed-point theorems.
December 31st, 1969
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