13,653 reputation
22063
bio website austinmohr.com
location Lincoln, NE
age 28
visits member for 2 years, 11 months
seen 2 hours ago

Status
Assistant Professor in the Department of Mathematics at Nebraska Wesleyan University

Interests
Combinatorics, general topology, and mathematics pedagogy

Currently Researching
Applications of the Lopsided Lovász Local Lemma

Spacebook
Spacebook is a searchable database of topological spaces and their properties (in ZFC) inspired by Steen and Seebach’s Counterexamples in Topology. (Learn more.)


2h
answered Cantor's Teepee is Totally Disconnected
7h
comment Variation of Nim: Player who takes last match loses
Saying "$n = 4j+1$ for some integer" is the same as saying "$n \equiv 1$ (mod 4)". Similarly for the other examples.
1d
revised Cantor's Teepee is Totally Disconnected
explaining my confusion
1d
accepted Cantor's Teepee is Totally Disconnected
1d
comment How many non-isomorphic, connected graphs are there on $n$ vertices with $k$ edges?
possible duplicate of How many non-isomorphic graphs with n vertices and m edges are there?
1d
comment Cantor's Teepee is Totally Disconnected
@studiosus I left off "whose union is the entire space", but I take it even this revision would be incorrect. I think you have helped me identify my confusion, however, so please tell me if the following is correct: If I want to show a subset S of the teepee is disconnected, I need to demonstrate separated sets A and B whose union is S, not necessarily the entire teepee. The sets A and B should be open in the subspace topology induced by S, not necessarily open in the teepee's topology. (The bold, if correct, is the key new realization for me.)
1d
comment Cantor's Teepee is Totally Disconnected
Am I incorrect in understanding that "totally disconnected" means "for any two points in the space, there are separated open sets each containing one of the points"?
2d
comment Cantor's Teepee is Totally Disconnected
Another commenter noted that the author of that thesis is using a nonstandard definition of "totally disconnected".
2d
comment Cantor's Teepee is Totally Disconnected
What would be the open set in the usual topology on $\mathbb{R}^2$ whose intersection with the teepee is $B$? That is to say, I don't think $B$ is open in the subspace topology.
2d
revised Cantor's Teepee is Totally Disconnected
deleted 235 characters in body; edited title
2d
comment Cantor's Teepee is Totally Disconnected
@cheapeffectivedietpills I think you are correct. Thanks for pointing that out.
2d
comment Cantor's Teepee is Totally Disconnected
@cheapeffectivedietpills Rather than define the "leaky tent" and the remove the point $(1/2,1/2)$ to obtain the teepee, I removed the point from the beginning by explicitly defining $L(c)$ to exclude $(1/2,1/2)$. I saw the MathOverflow question, but it does not contain a proof of total disconnectedness.
2d
revised Cantor's Teepee is Totally Disconnected
added 43 characters in body
2d
revised Cantor's Teepee is Totally Disconnected
added 45 characters in body
2d
comment Cantor's Teepee is Totally Disconnected
@AlexBecker I've updated the definition to include $(0,0)$ and $(1,0)$ as endpoints. Whether they are included or not should not affect the total disconnectedness.
2d
revised Cantor's Teepee is Totally Disconnected
added 58 characters in body
2d
asked Cantor's Teepee is Totally Disconnected
Apr
12
revised Please check my child's homework, what are the correct answers?
clarity
Mar
18
accepted Text on Group Theory and Graphs
Mar
13
awarded  graph-theory