871 - Topology
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Revision as of 17:02, 7 December 2022 by Kfagerstrom (talk | contribs) (Created page with " ==Homeomorphism Invariants== ===Metrizability=== ===Connectedness=== ===Path Connected=== ===Compactness=== ===<math>Separation Properties </math>=== ====<math>T_1 </m...")
Contents
Homeomorphism Invariants
Metrizability
Connectedness
Path Connected
Compactness
\(Separation Properties \)
\(T_1 \)
A topological space \(X \) is \(T_1 \) if for any two distinct points \( a,b\in X\) there are open sets \( U,V\) in \(X \) with \(a\in U, b\not \in U, a\not\in V, b\in V \).
\(T_2 \) (Hausdorff)
\(T_3 \) (Regular)
A topological space \(X \) is \(T_3 \) if it is \(T_1 \) and for any point \( a \in X\) and closed set \(B \in X \) with \(a \not \in B \), there are disjoint open sets \(U,V \in X \) with \(a\in U \) and \(B\sube V \)
\(T_4 \) (Normal)
A topological space \(X \) is \(T_4 \) if it is \(T_1 \)and for any two disjoint closed sets \(A,B \in X \) there are disjoint open sets \(U,V \in X \) with \( A \sube U\) and \(B \sube V \).
