Topological space
Concept history
A revision trail for this concept page.
Revision 7740
10/24/2026, 7:00:33 PM · Ancient Tree
Shared settings updated from fr translation
domainTopologyTopology
Revision 5680
9/23/2026, 3:05:27 PM · SalixBabylonica
Added exercise "Les ouverts d'un espace métrique forment une topologie"
linked exercisesNoneLes ouverts d’un espace métrique forment une topologie
Revision 664
7/27/2026, 12:47:06 PM · Ancient Tree
Concept edited
This older revision predates detailed metadata tracking.
Revision 663
7/27/2026, 12:46:39 PM · Ancient Tree
Concept edited
Compare with revision 1795 changed lines
1
A topological space is...1
A topological space is a [[Set|set]] $X$ together with a [[topology|topology]] $\tau$, that is, a collection of subsets of $X$, called the [[Open set|open sets]], satisfying the following axioms:2
1. The [[Empty set|empty set]] and the whole space are open: $\emptyset\in \tau$ and $X\in \tau$.3
2. [[Arbitrary union|Arbitrary unions]] of open sets are open: if $\{U_{i}\}_{i\in I}$ is any family of sets in $\tau$, then $\bigcup_{i \in I} U_i \in \tau$.4
3. Finite [[Intersection of sets|intersections]] of open sets are open: if $U_1, \ldots, U_n \in \tau$, then $U_1 \cap \cdots \cap U_n \in \tau$.Revision 179
7/1/2026, 1:37:07 PM · Ancient Tree
Concept created
A topological space is...