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- General_topology abstract "In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geometric topology, and algebraic topology. Another name for general topology is point-set topology.The fundamental concepts in point-set topology are continuity, compactness, and connectedness: Continuous functions, intuitively, take nearby points to nearby points. Compact sets are those that can be covered by finitely many sets of arbitrarily small size. Connected sets are sets that cannot be divided into two pieces that are far apart. The words 'nearby', 'arbitrarily small', and 'far apart' can all be made precise by using open sets, as described below. If we change the definition of 'open set', we change what continuous functions, compact sets, and connected sets are. Each choice of definition for 'open set' is called a topology. A set with a topology is called a topological space.Metric spaces are an important class of topological spaces where distances can be assigned a number called a metric. Having a metric simplifies many proofs, and many of the most common topological spaces are metric spaces.".
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- General_topology wikiPageWikiLink (ε,_δ)-definition_of_limit.
- General_topology wikiPageWikiLink Algebra_over_a_field.
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- General_topology wikiPageWikiLink Algebraic_variety.
- General_topology wikiPageWikiLink ArXiv.
- General_topology wikiPageWikiLink Associative_algebra.
- General_topology wikiPageWikiLink Axiom_of_countable_choice.
- General_topology wikiPageWikiLink Baire_category_theorem.
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- General_topology wikiPageWikiLink Ball_(mathematics).
- General_topology wikiPageWikiLink Base_(topology).
- General_topology wikiPageWikiLink Bijection.
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- General_topology wikiPageWikiLink Boundary_(topology).
- General_topology wikiPageWikiLink Bourbaki.
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- General_topology wikiPageWikiLink Function_(mathematics).
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- General_topology wikiPageWikiLink Heine–Borel_theorem.
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