Review Note
Last Update: 04/24/2024 02:36 AM
Current Deck: Topology
PublishedCurrently Published Content
Premise 1
\(X\) is a set
\( \mathcal T \in \mathcal P (X)\) such that
\( \mathcal T \in \mathcal P (X)\) such that
Consequence 1
\(\emptyset \in \mathcal T\)
Consequence 2
\(X \in \mathcal T\)
Consequence 3
Closure under finite intersections: if \(U \in \mathcal T\) and \(V \in \mathcal T\), then \(U \cap V \in \mathcal T\)
Consequence 4
Closure under arbitrary union: if \(\set{U_\alpha}_{\alpha \in \lambda} \) is an arbitrary family of subsets of \( \mathcal T\), then \(\bigcup_{\alpha \in \lambda} U_\alpha \in \mathcal T\)
Consequence 5
Name
Topology
Context
Subcontext
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