| Title: | General topology |
|---|---|
| Description: | These notes on the basic notions of topological spaces were written by Jesper M. Moller for a course for undergraduate students at the University of Copenhagen. The first chapter reviews topics in set theory which are required during this course. It concludes with Zorn's lemma. The second chapter introduces topological spaces. Various ways to construct new topological spaces from old ones, such as products or subsets of topological spaces, are discussed. Metric spaces are introduced. Compactness and connectedness are amongst the first important properties that a topological space may have. These notions are introduced at the end of the second chapter, which concludes with the notion of local compactness and Alexandroff compactification. The third chapter discusses the separation axioms, and considers regular and normal spaces (T3 and T4 spaces). T1 and T2 (Hausdorff) spaces are reviewed. It also considers Stone-Cech compactification of a topological space. The notion of a manifold is introduced. Having some background in analysis and metric spaces could be very useful to the reader. |
| Keywords - uncontrolled: | topology; sets; maps; relations; integers; real numbers; products; coproducts; finite sets; infinite sets; countable sets; uncountable sets; well-ordered sets; partially ordered sets; Maximum Principle; Zorns lemma; topological spaces; continuous maps; order topology; product topology; subspace topology; interiors; open sets; closed sets; limit points; isolated points; continuous functions; homeomorphisms; embedding; quotient topology; metric topology; connected spaces; compact spaces; locally compact spaces; Alexandroff compactification; regular spaces; normal spaces; Urysohn metrisation theorem; completely regular spaces; StoneCech compactification; manifolds; equivalence relations; immediate predecessors; immediate successors; upper bounds; lower bounds; quotient maps; adjunction spaces; Whitehead theorem; uniform metric; path connected space; locally path connected space; Closed Map Lemma; Tube Lemma |
| Type: | Lecture notes |
| URL: | http://www.math.ku.dk/~moller/e03/3gt/notes/gtnotes.pdf |
| Classification: |
Mathematics and computer science > Mathematics > Geometry and topology > Topology |
| Resource creator: | Moller, Jesper M. |
| Country of origin: | Denmark |
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