**Quick Tour of the Topology of R**

by StevenHurder, DaveMarker

**Publisher**: University of Illinois at Chicago 2003**Number of pages**: 48

**Description**:

These notes are a supplement for the 'standard undergraduate course' in Analysis at the University of Illinois at Chicago. The aim is to present a more general perspective on the incipient ideas of topology encountered when exploring the rigorous theorem-proof approach to the results of Calculus.

Download or read it online for free here:

**Download link**

(370KB, PDF)

## Similar books

**Homeomorphisms in Analysis**

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.

(

**10162**views)

**Notes on Introductory Point-Set Topology**

by

**Allen Hatcher**-

**Cornell University**

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.

(

**3704**views)

**Topology Without Tears**

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.

(

**12398**views)

**Nonstandard Analysis in Topology**

by

**Sergio Salbany, Todor Todorov**-

**arXiv**

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 seem to be new in the literature.

(

**6150**views)