Skip to main content
Search type Search syntax
Tags [tag]
Exact "words here"
Author user:1234
user:me (yours)
Score score:3 (3+)
score:0 (none)
Answers answers:3 (3+)
answers:0 (none)
isaccepted:yes
hasaccepted:no
inquestion:1234
Views views:250
Code code:"if (foo != bar)"
Sections title:apples
body:"apples oranges"
URL url:"*.example.com"
Saves in:saves
Status closed:yes
duplicate:no
migrated:no
wiki:no
Types is:question
is:answer
Exclude -[tag]
-apples
For more details on advanced search visit our help page
Results tagged with
Search options questions only not deleted user 2362

Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.

13 votes
0 answers
255 views

Big list of Hochster dual concepts

Let $X$ be a spectral space. Then there is a canonical space $X^\vee$ with the same points, same constructible topology, and the opposite specialization order. This is known as “Hochster duality”, and …
7 votes
2 answers
197 views

Cover the $n$-disc irredundantly with $n+1$ open sets. Suppose that the $(n+1)$-fold interse...

Cover the $n$-disc with $n+1$ open sets $D^n = U_0 \cup \dotsb \cup U_n$. Suppose that $U_0 \cap \dotsb \cap U_n = \emptyset$. Suppose moreover that the cover is irredundant in the sense that no prope …
Tim Campion's user avatar
11 votes
1 answer
709 views

On the classification of second-countable Stone spaces

Let $X$ be a Stone space (i.e. totally disconnected compact Hausdorff). Then the following are equivalent: $X$ is second countable $X$ is metrizable $X$ has countably many clopen subsets $X$ is an in …
Tim Campion's user avatar
5 votes
0 answers
131 views

Is the opposite of the category of $\kappa$-Lindelöf Hausdorff spaces locally presentable?

Gelfand duality tells us that the category of compact Hausdorff spaces (with continuous maps as morphisms) is contravariantly equivalent to the category of commutative, unital $C^\ast$-algebras (with …
Tim Campion's user avatar
6 votes
1 answer
451 views

Which maps of topological spaces have the right lifting property with respect to all split m...

Let $p : X \to Y$ be a continuous map. We say that $p$ has the right lifting property with respect to split monomorphisms if, for every space $B$, and every retract $A \subseteq B$, and for every cont …
Tim Campion's user avatar
1 vote
0 answers
99 views

"Classifying" causally closed sets in Minkowski space

Let $M = \mathbb R^{D+1}$ be Minkowski space. Recall that the causal complement of a set $A \subseteq M$ is the set $A^\perp \subseteq M$ where $p \in A^\perp$ there is no timelike path between $p$ an …
Tim Campion's user avatar
6 votes
0 answers
187 views

What is a non-smooth connection?

Let $p : E \to B$ be a map of topological spaces, and $p^I : E^I \to B^I$ the induced map of path spaces. Let $Cocyl(p) = B^I \times_B E$ be the space of paths $\beta$ in $B$ equipped with a lift of $ …
Tim Campion's user avatar
5 votes
0 answers
203 views

What are all of the topological (commutative) monoid structures on a closed interval?

Consider a closed real interval $[a,b]$ as a toplogical space. Up to homeomeorphism it doesn't matter, but I like to take $[a,b] = [0,\infty]$. Question 1: What are all of the topological commutative …
Tim Campion's user avatar
4 votes
1 answer
796 views

How do finite door spaces work?

Recall that a door space is a topological space where every set is either open or closed (or both). A topological space is finite if it has finitely many points. I'm interested in learning about finit …
Tim Campion's user avatar
15 votes
1 answer
467 views

What are the algebras for the ultrafilter monad on topological spaces?

Motivation: Let $(X,\tau)$ be a topological space. Then the set $\beta X$ of ultrafilters on $X$ admits a natural topology (cf. Example 5.14 in Adámek and Sousa - D-ultrafilters and their monads), giv …
Tim Campion's user avatar
7 votes
0 answers
262 views

When is the exponential of a map proper?

Let $X$ be a compact Hausdorff space. Then if $f: A \to B$ is a map between discrete spaces, the induced map $f^\ast: X^B \to X^A$ is proper. Question: Are there other classes of map $f: A \to B$ suc …
Tim Campion's user avatar
36 votes
1 answer
3k views

Is there a general theory of "compactification"?

In various branches of mathematics one finds diverse notions of compactification, used for diverse purposes. Certainly one does not expect all instances of "compactification" to be specializations of …
Tim Campion's user avatar
15 votes
3 answers
1k views

What do absolute neighborhood retracts look like?

In the course of filling in my map of non-pathological topology, I'd like to understand the class of ANRs (Absolute Neighborhood Retracts) as a sort of "neighborhood" of the class of CW complexes. Thi …
Tim Campion's user avatar
1 vote
1 answer
437 views

Topology of length spaces

How wild can the topology of a length space be? That is, Questions: Let $X$ be a metric space where the distance between two points $x,y \in X$ is the infinum of lengths of rectifiable paths from …
Tim Campion's user avatar
40 votes
3 answers
3k views

A map of non-pathological topology?

I think of topological spaces as coming in several "islands of interestingness" (the CW island, the Zariski archipelago,...) dotting a vast "pathological sea" (the long line ocean, the gulf of the low …
Tim Campion's user avatar

15 30 50 per page