Problem: Show that if is a basis for a topology on , then the topology generated by equals the intersection of all topologies on that contain . 159 more words
As an introductory remark for this being my first set of problems from the Munkres text, I have a few things to note.
I want to point out why fundamental groups are defined for loops, and not path homotopy classes. This is something that Munkres’ Topology does not do a good job of explaining. 153 more words
Okay, so this post is going to be pretty much like the rest of the posts recently:
I’ll write about something awesome I did recently, then I’ll make a tongue-in-cheek allusion to a metaphor about life, and then I’ll mention that I haven’t found any jobs, or really started looking, but then I’ll talk about how I’ve been doing other interesting things. 418 more words