solid torus

solid torus
a) The topological space that is a Cartesian product of the 2-dimensional disk and the circle.
b) The standard representation of that topological space within Euclidean 3-dimensional space.

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  • Solid torus — In mathematics, a solid torus is a topological space homeomorphic to S^1 imes D^2, i.e. the cartesian product of the circle with a two dimensional disc endowed with the product topology. The solid torus is a connected, compact, orientable 3… …   Wikipedia

  • Torus — Not to be confused with Taurus (disambiguation). This article is about the surface and mathematical concept of a torus. For other uses, see Torus (disambiguation). A torus As the distance to th …   Wikipedia

  • Torus — To rus (t[=o] r[u^]s), n.; pl. {Tori} (t[=o] r[imac]). [L., a round, swelling, or bulging place, an elevation. Cf. 3d {Tore}.] [1913 Webster] 1. (Arch.) A large molding used in the bases of columns. Its profile is semicircular. See Illust. of… …   The Collaborative International Dictionary of English

  • torus — [tō′rəs, tôr′əs] n. pl. tori [tôr′rī΄, tôr′ī] [L, a bulge, muscle] 1. Anat. any rounded projection or swelling 2. Archit. a large, convex molding used at the base of columns, etc., just above the plinth 3. Bot. a) RECEPTACLE (sense 3a) …   English World dictionary

  • -holed solid torus — noun A three dimensional topological space that is a handlebody with the specified number of 1 handles …   Wiktionary

  • torus — solid geometrical figure with the shape of a doughnut or innertube, as in the toroidal hydrogen cloud surrounding Saturn near the orbit of Titan …   Mechanics glossary

  • torus — /ˈtɔrəs/ (say tawruhs) noun (plural tori /ˈtɔraɪ/ (say tawruy)) 1. Architecture a large convex moulding, more or less semicircular in profile, commonly forming the lowest member of the base of a column, or that directly above the plinth (when… …  

  • torus — /tawr euhs, tohr /, n., pl. tori /tawr uy, tohr uy/. 1. Archit. a large convex molding, more or less semicircular in profile, commonly forming the lowest molding of the base of a column, directly above the plinth, sometimes occurring as one of a… …   Universalium

  • torus — [ tɔ:rəs] noun (plural tori rʌɪ or toruses) 1》 Geometry a surface or solid resembling a ring doughnut, formed by rotating a closed curve about a line which lies in the same plane but does not intersect it. 2》 a ring shaped object or chamber. 3》… …   English new terms dictionary

  • torus — to•rus [[t]ˈtɔr əs, ˈtoʊr [/t]] n. pl. to•ri [[t]ˈtɔr aɪ, ˈtoʊr aɪ[/t]] 1) archit. a large convex molding, semicircular in profile, commonly forming the lowest member of the base of a column, directly above the plinth 2) math. a) a doughnut… …   From formal English to slang

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