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seen May 5 '13 at 11:15

Jun
7
awarded  Critic
May
31
awarded  Scholar
May
31
accepted Is there a name for a collection of open sets where arbitrary intersections are open?
May
30
comment Is there a name for a collection of open sets where arbitrary intersections are open?
Excellent! On the odd chance that somebody comes along with a better answer, I'll wait a little before accepting.
May
30
awarded  Student
May
30
asked Is there a name for a collection of open sets where arbitrary intersections are open?
May
20
awarded  Editor
May
20
revised homotopy direct limits
Included pointer to the discussion in the comments.
May
20
comment homotopy direct limits
I believe you are correct. Your supposition that $X_\Sigma$ is a h-direct limit of the $U_i$ is at least valid. The space $X_\Sigma$ is in fact the direct limit of the $U_i$ and since all the inclusions $U_i \hookrightarrow U_{i+1}$ are cofibrations the direct limit and h-direct limit are the same. I will edit my answer and point the reader to your argument.
May
19
comment homotopy direct limits
Yes, that's exactly the map I had in mind, Tim! This answer to another question is related to our situation, but there the existence of a homotopy inverse is guaranteed by an algebraic argument.
May
19
answered homotopy direct limits
Jun
11
comment How to study math to really understand it and have a healthy lifestyle with free time?
This really struck a nerve in the community here; no other questions produces 6 lengthy answers in 6 hours! So @Leon: Cherish the fact that you're not alone in this situation until you find a remedy. :)
Jan
28
awarded  Supporter
Nov
10
answered How many ways can I make six moves on a Rubik's cube?
Oct
17
comment Book about technical and academic writing
reddit.com/r/math/comments/9wdzo/… If you google the title of the book you will find one version, but the typesetting is so ugly you wouldn't want to read it!
Oct
17
awarded  Teacher
Oct
17
answered Book about technical and academic writing