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Jacob Harvey Mason

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

Howard County

Why fundamental groups are defined only for loops- better explained than in Munkres' Topology.

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

You Haunt Me

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

Stories

Munkres 26

1a. Let and be two topologies on the set ; Suppose that .  What does compactness if under one topology say about compactness in the other? 966 more words

Topology

Munkres 25

1. What are the components and path components of ?  What are the continuous maps ?

Given in , separate and show that must be in different components.   734 more words

Topology

Munkres 24

1a. Show that no two of the spaces , , and are homeomorphic.

All three spaces are connected.  Deleting any point from gives a disconnected space.   1,055 more words

Topology

Munkres 23

1. If and are two topologies on with , what does connectedness of in one topology imply about connectedness in the other?

If is connected under , it must necessarily be connected under because a separation in is also a separation in .   364 more words

Topology