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Mathematics · L5 · Point-Set Topology: Open Sets, Continuity, and Compactness · flowchart

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by @openstemUpdated Mathematics
Metric space (X, d)Induces a topology τ(open balls define open sets)Properties of (X, τ)Hausdorff?Separate points by open setsConnected?No nontrivial clopen subsetCompact?Every open cover hasa finite subcoverIn ℝⁿ: compact ⟺closed and bounded

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