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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.
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