Nonstandard Analysis in Topology
by Sergio Salbany, Todor Todorov
Publisher: arXiv 2011
Number of pages: 48
We present Nonstandard Analysis in the framework of the superstructure of a given infinite set. We also present several applications of this axiomatic approach to point-set topology. Some of the topological topics such as the Hewitt real compactification and the nonstandard characterization of the sober spaces seem to be new in the literature on nonstandard analysis.
Home page url
Download or read it online for free here:
by Peter Saveliev - Intelligent Perception
This is an introductory, one semester course on point-set topology and applications. Topics: topologies, separation axioms, connectedness, compactness, continuity, metric spaces. Intended for advanced undergraduate and beginning graduate students.
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 Alex Kuronya
Contents: Basic concepts; Constructing topologies; Connectedness; Separation axioms and the Hausdorff property; Compactness and its relatives; Quotient spaces; Homotopy; The fundamental group and some applications; Covering spaces; etc.
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.