
Recent Posts
Archives
 May 2020
 April 2020
 March 2020
 June 2018
 July 2016
 June 2016
 May 2016
 March 2015
 February 2015
 January 2015
 December 2014
 December 2013
 November 2013
 July 2013
 June 2013
 May 2013
 March 2013
 February 2013
 January 2013
 December 2012
 November 2012
 October 2012
 September 2012
 August 2012
 April 2012
 March 2012
 February 2012
 January 2012
 December 2011
 November 2011
 October 2011
Categories
Meta
Pages
Tag Archives: separation axioms
Topology: Topological Groups
This article assumes you know some basic group theory. The motivation here is to consider groups whose underlying operations are continuous with respect to its topology. Definition. A topological group G is a group with an underlying topology such that: the … Continue reading
Posted in Notes
Tagged advanced, compact sets, connected components, groups, homeomorphisms, separation axioms, topological groups, topology
Leave a comment
Topology: Separation Axioms
Motivation The separation axioms attempt to answer the following. Question. Given a topological space X, how far is it from being metrisable? We had a hint earlier: all metric spaces are Hausdorff, i.e. distinct points can be separated by two … Continue reading
Posted in Notes
Tagged advanced, Hausdorff, metrisable topology, normal, regular, separation axioms, T1, T2, T3, T4, topology, urysohn's lemma, urysohn's metrisation theorem
Leave a comment