**2.13.5**

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

**2.13.5**

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.

- The numbering system corresponds as follows: “<chapter>.<section>.<problem number>”. 254 more words

Happy to all around the world!

This past year is been a huge part in the growth of my blog. To ramble about the statistics, we nearly doubled the of amount views [ () to ()] and doubled the amount of visitors [ () to ()]. 261 more words

**Jacob Harvey Mason**

b. 6 July 1856, Ervin Township, Howard County, Indiana, to Simon Peter and Elizabeth (White) Mason

d. 7 March 1903, southeastern Woods County, Oklahoma Territory (now Major County) 184 more words

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