Graph (topology) (original) (raw)
In topology, a branch of mathematics, a graph is a topological space which arises from a usual graph by replacing vertices by points and each edge by a copy of the unit interval , where is identified with the point associated to and with the point associated to . That is, as topological spaces, graphs are exactly the simplicial 1-complexes and also exactly the one-dimensional CW complexes. Thus, in particular, it bears the quotient topology of the set The topology on this space is called the graph topology.
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| dbo:abstract | In topology, a branch of mathematics, a graph is a topological space which arises from a usual graph by replacing vertices by points and each edge by a copy of the unit interval , where is identified with the point associated to and with the point associated to . That is, as topological spaces, graphs are exactly the simplicial 1-complexes and also exactly the one-dimensional CW complexes. Thus, in particular, it bears the quotient topology of the set under the quotient map used for gluing. Here is the 0-skeleton (consisting of one point for each vertex ), are the intervals ("closed one-dimensional unit balls") glued to it, one for each edge , and is the disjoint union. The topology on this space is called the graph topology. (en) |
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| dbo:wikiPageRevisionID | 1084951032 (xsd:integer) |
| dbo:wikiPageWikiLink | dbr:Homotopy_equivalence dbr:Connectivity_(graph_theory) dbr:Mathematics dbr:Circle dbr:Graph_(discrete_mathematics) dbr:Connected_space dbr:Bijective dbr:Functor dbr:Fundamental_group dbr:Wedge_sum dbc:Topological_spaces dbr:Topology dbr:Graph_homology dbr:Simplicial_complex dbr:Interval_(mathematics) dbr:Covering_space dbr:Disjoint_union dbr:CW_complex dbr:Free_group dbr:If_and_only_if dbr:Category_(mathematics) dbr:Category_of_topological_spaces dbr:Set_(mathematics) dbr:Unit_interval dbr:Maximal_element dbr:Nielsen–Schreier_theorem dbr:Subspace_topology dbr:Topological_space dbr:Topological_graph_theory dbr:Quotient_topology |
| dbp:wikiPageUsesTemplate | dbt:Short_description |
| dct:subject | dbc:Topological_spaces |
| rdfs:comment | In topology, a branch of mathematics, a graph is a topological space which arises from a usual graph by replacing vertices by points and each edge by a copy of the unit interval , where is identified with the point associated to and with the point associated to . That is, as topological spaces, graphs are exactly the simplicial 1-complexes and also exactly the one-dimensional CW complexes. Thus, in particular, it bears the quotient topology of the set The topology on this space is called the graph topology. (en) |
| rdfs:label | Graph (topology) (en) |
| owl:sameAs | wikidata:Graph (topology) https://global.dbpedia.org/id/2qzNQ |
| prov:wasDerivedFrom | wikipedia-en:Graph_(topology)?oldid=1084951032&ns=0 |
| foaf:isPrimaryTopicOf | wikipedia-en:Graph_(topology) |
| is dbo:wikiPageDisambiguates of | dbr:Graph |
| is dbo:wikiPageWikiLink of | dbr:Node_graph_architecture dbr:Configuration_space_(mathematics) dbr:Graph_homology dbr:Graph |
| is rdfs:seeAlso of | dbr:Topological_graph_theory |
| is foaf:primaryTopic of | wikipedia-en:Graph_(topology) |