Notes on Introductory Point-Set Topology
by Allen Hatcher
Publisher: Cornell University 2011
Number of pages: 53
These are lecture notes from the first part of an undergraduate course in 2005, covering just the most basic things. From the table of contents: Basic Point-Set Topology; Connectedness; Compactness; Quotient Spaces; Exercises.
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by T. W. Körner - University of Cambridge
Contents: What is a metric?; Examples of metric spaces; Continuity and open sets for metric spaces; Closed sets for metric spaces; Topological spaces; Interior and closure; More on topological structures; Hausdorff spaces; Compactness; etc.
by StevenHurder, DaveMarker - University of Illinois at Chicago
These notes are a supplement for the 'standard undergraduate course' in Analysis. The aim is to present a more general perspective on the incipient ideas of topology encountered when exploring the rigorous theorem-proof approach to Calculus.
by Sidney A. Morris
It provides a thorough grounding in general topology: introduction, topological spaces, the Euclidian topology, limit points, homeomorphisms, continuous mappings, metric spaces, compactness, finite products, countable products, Tychonoff's theorem.
by O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov - American Mathematical Society
This textbook on elementary topology contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment centered at the notions of fundamental group and covering space.