General topology

Filter to Topological vector bundle

• Filter
• Limit of a map with respect to filters
• Topological space
• Continuous function
• The category of topological spaces
• Induced topology
• Open map
• Closed map
• Closure
• Cluster point
• Hausdorff space
• Sequential space
• Extension by continuity
• Compactness in terms of filters
• Compactness in terms of open covers (Borel-Lebesgue)
• Connectedness
• Compact open topology
• Stone-Cech compactification
• Topological fiber bundle
• Topological vector bundle

Urysohn's lemma to Stone-Weierstrass theorem

• Urysohn's lemma
• Stone-Weierstrass theorem

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