Document Type

Course Materials

Publication Date

Spring 2016


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

Primary Source Author(s)

Georg Cantor