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Types of Topological Spaces
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Second-Countable Space
A topological space that has a countable base for its topology.
Hausdorff Space (T2 Space)
A topological space where any two distinct points have disjoint open neighborhoods.
Locally Compact Space
A topological space where every point has a compact neighborhood.
Path-Connected Space
A topological space where any two points can be connected by a path within the space.
First-Countable Space
A topological space where each point has a countable basis of neighborhoods.
Connected Space
A topological space that cannot be represented as a union of two or more disjoint non-empty open sets.
Compact Space
A topological space where every open cover has a finite subcover.
Metric Space
A topological space which has a metric (distance function) that defines the topology.
Normal Space (T4 Space)
A topological space in which any two disjoint closed sets have disjoint open neighborhoods.
Complete Metric Space
A metric space in which every Cauchy sequence converges to a limit within the space.
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