| dbo:abstract |
In mathematics, a strong topology is a topology which is stronger than some other "default" topology. This term is used to describe different topologies depending on context, and it may refer to: * the final topology on the disjoint union * the topology arising from a norm * the strong operator topology * the strong topology (polar topology), which subsumes all topologies above. A topology τ is stronger than a topology σ (is a finer topology) if τ contains all the open sets of σ. In algebraic geometry, it usually means the topology of an algebraic variety as complex manifold or subspace of complex projective space, as opposed to the Zariski topology (which is rarely even a Hausdorff space). (en) 数学における強位相（きょういそう、英: strong topology）とは、他の「元来の」位相よりも強い位相である。通常、文脈によって次のような異なる位相のことを指す。 * 直和上の * ノルムより生じる位相 * 強作用素位相 * これらすべてを含む強位相 (極位相) 位相 τ が位相 σ よりも強い（である）とは、τ が σ のすべての開集合を含むことを言う。 代数幾何学において強位相は通常、ハウスドルフ空間であることすら稀なザリスキー位相とは対照的に、代数多様体の複素多様体としての位相、あるいは複素射影空間の部分空間としての位相を表す。 (ja) |
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dbr:Mathematics dbr:Comparison_of_topologies dbr:Complex_manifold dbr:Complex_projective_space dbr:Topology dbr:Weak_topology dbr:Disjoint_union_(topology) dbr:Hausdorff_space dbr:Algebraic_geometry dbr:Algebraic_variety dbc:Topology dbr:Strong_topology_(polar_topology) dbr:Final_topology dbr:Strong_operator_topology dbr:Zariski_topology dbr:Normed_vector_space |
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dbt:Sia |
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dbc:Topology |
| gold:hypernym |
dbr:Topology |
| rdfs:comment |
数学における強位相（きょういそう、英: strong topology）とは、他の「元来の」位相よりも強い位相である。通常、文脈によって次のような異なる位相のことを指す。 * 直和上の * ノルムより生じる位相 * 強作用素位相 * これらすべてを含む強位相 (極位相) 位相 τ が位相 σ よりも強い（である）とは、τ が σ のすべての開集合を含むことを言う。 代数幾何学において強位相は通常、ハウスドルフ空間であることすら稀なザリスキー位相とは対照的に、代数多様体の複素多様体としての位相、あるいは複素射影空間の部分空間としての位相を表す。 (ja) In mathematics, a strong topology is a topology which is stronger than some other "default" topology. This term is used to describe different topologies depending on context, and it may refer to: * the final topology on the disjoint union * the topology arising from a norm * the strong operator topology * the strong topology (polar topology), which subsumes all topologies above. A topology τ is stronger than a topology σ (is a finer topology) if τ contains all the open sets of σ. (en) |
| rdfs:label |
Topologia forte (it) 強位相 (ja) Strong topology (en) |
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