Topology and subsets - the story of a theorem

Abstract

In this exposition the space of at most 3-element subsets of the circle, first identified by Borsuk and Bott, is used as a motivation to introduce the readers to a variety of methods in (algebraic) topology.

This article is a translation of the original (in Polish), written for Matematyka, Spoleczenstwo, Nauczanie, Vol.46. It is an extended version of the talk by the author at the XLV Szkola Matematyki Pogladowej, Jachranka, Poland, 27-31 August 2010, see http://www.msn.ap.siedlce.pl