Separated sets
Type of relation for subsets of a topological space / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Separated sets?
Summarize this article for a 10 year old
SHOW ALL QUESTIONS
In topology and related branches of mathematics, separated sets are pairs of subsets of a given topological space that are related to each other in a certain way: roughly speaking, neither overlapping nor touching. The notion of when two sets are separated or not is important both to the notion of connected spaces (and their connected components) as well as to the separation axioms for topological spaces.
Quick Facts Separation axioms in topological spaces, Kolmogorov classification ...
Separation axioms in topological spaces | |
---|---|
Kolmogorov classification | |
T0 | (Kolmogorov) |
T1 | (Fréchet) |
T2 | (Hausdorff) |
T2½ | (Urysohn) |
completely T2 | (completely Hausdorff) |
T3 | (regular Hausdorff) |
T3½ | (Tychonoff) |
T4 | (normal Hausdorff) |
T5 | (completely normal Hausdorff) |
T6 | (perfectly normal Hausdorff) |
Close
This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these template messages)
|
Separated sets should not be confused with separated spaces (defined below), which are somewhat related but different. Separable spaces are again a completely different topological concept.