Filters, part III: pretopologies

While listening to some talks at the special session on categorical topology last Saturday, I realized that I had said something wrong at the end of part II: the filter spaces satisfying the property that any intersection of filters that converge to a point x must also converge to x are not the topological filter spaces, but the pretopological filter spaces.  See the full post for an in-depth discussion of the matter.

 

Joint Mathematics Meetings

I’m currently at the Joint Mathematics Meeting in Baltimore, MD, USA.  This is a huge conference.  The program alone is a 250+ page booklet!

My main purpose there is to participate in the special session on categorical topology on Saturday, January 18th.  I’m going to talk about the Escardò-Lawson-Simpson construction (Section 5.6 in the book).  Nicely enough, this generalizes outside of pure topology, by the mere virtue of so-called topological functors.  I’m also applying all that to Sanjeevi Krishnan’s notion of streams, an incredibly nice model for directed algebraic topology.  You can find all this in my slides.  If you are brave, you can also read the paper.

Next week, I’ll visit Frédéric Mynard at Georgia Southern University, Statesboro, GA, USA.  On Tuesday, January 21st, I’ll give a related talk that is meant as an introduction to directed algebraic topology and streams.