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.
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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 Casper Goffman, at al. - American Mathematical Society
This book features the interplay of two main branches of mathematics: topology and real analysis. The text covers Lebesgue measurability, Baire classes of functions, differentiability, the Blumberg theorem, various theorems on Fourier series, etc.
by David Wilkins - Trinity College, Dublin
The lecture notes for course 212 (Topology), taught at Trinity College, Dublin. Topics covered: Limits and Continuity, Open and Closed Sets, Metric Spaces, Topological Spaces, Normed Vector Spaces and Functional Analysis, Topology in the Plane.
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.