Download PDF

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

General topology wikipedia, lookup

Fundamental group wikipedia, lookup

Covering space wikipedia, lookup

Transcript
T1 space∗
drini†
2013-03-21 13:26:22
A topological space (X, τ ) is said to be T1 (or said to hold the T1 axiom) if
for all distinct points x, y ∈ X (x 6= y), there exists an open set U ∈ τ such that
x ∈ U and y ∈
/ U.
A space being T1 is equivalent to the following statements:
• For every x ∈ X, the set {x} is closed.
• Every subset of X is equal to the intersection of all the open sets that
contain it.
• Distinct points are separated.
∗ hT1Spacei created: h2013-03-21i by: hdrinii version: h31852i Privacy setting: h1i
hDefinitioni h54D10i
† This text is available under the Creative Commons Attribution/Share-Alike License 3.0.
You can reuse this document or portions thereof only if you do so under terms that are
compatible with the CC-BY-SA license.
1