Document Type
Course Materials
Publication Date
Spring 2016
Abstract
Topology is often described as having no notion of distance, but a notion of nearness. How can such a thing be possible? Isn't this just a distinction without a diff erence? In this project, we will discover the notion of nearness without distance by studying the work of Georg Cantor and a problem he was investigating involving Fourier series. We will see that it is the relationship of points to each other, and not their distances per se, that is a proper view. We will see the roots of topology organically springing from analysis.
Applicable Math Courses
topology, analysis
Academic Division
Upper Division Undergraduate
Creative Commons License
This work is licensed under a Creative Commons Attribution-Share Alike 4.0 International License.
Recommended Citation
Scoville, Nicholas A., "Topology From Analysis" (2016). Topology. 1.
https://digitalcommons.ursinus.edu/triumphs_topology/1
Included in
Curriculum and Instruction Commons, Educational Methods Commons, Geometry and Topology Commons, Higher Education Commons, Science and Mathematics Education Commons
