# Solid Klein bottle

Solid Klein bottle

In mathematics, a solid Klein bottle is a 3-manifold (with boundary) homeomorphic to the quotient space obtained by gluing the top of $D^2 imes I$ (cylinder) to the bottom by a reflection, i.e. the point $\left(x,0\right),$ is identified with $\left(r\left(x\right), 1\right),$ where $r,$ is reflection of the disc $D^2,$ across a diameter.

Note the boundary of the solid Klein bottle is a Klein bottle.

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Orientability — For orientation of vector spaces, see orientation (mathematics). For other uses, see Orientation (disambiguation). The torus is an orientable surface …   Wikipedia

• List of manifolds — This is a list of particular manifolds, by Wikipedia page. See also list of geometric topology topics. For categorical listings see and its subcategories.Generic families of manifolds*Euclidean space, R n * n sphere, S n * n torus, T n *Real… …   Wikipedia

• List of mathematics articles (S) — NOTOC S S duality S matrix S plane S transform S unit S.O.S. Mathematics SA subgroup Saccheri quadrilateral Sacks spiral Sacred geometry Saddle node bifurcation Saddle point Saddle surface Sadleirian Professor of Pure Mathematics Safe prime Safe… …   Wikipedia

• Manifold — For other uses, see Manifold (disambiguation). The sphere (surface of a ball) is a two dimensional manifold since it can be represented by a collection of two dimensional maps. In mathematics (specifically in differential geometry and topology),… …   Wikipedia

• Surface — This article discusses surfaces from the point of view of topology. For other uses, see Differential geometry of surfaces, algebraic surface, and Surface (disambiguation). An open surface with X , Y , and Z contours shown. In mathematics,… …   Wikipedia

• topology — topologic /top euh loj ik/, topological, adj. topologically, adv. topologist, n. /teuh pol euh jee/, n., pl. topologies for 3. Math. 1. the study of those properties of geometric forms that remain invariant under c …   Universalium

• Fourth dimension — [ tesseract rotating around a plane in 4D.] In physics and mathematics, a sequence of n numbers can be understood as a location in an n dimensional space. When n =4, the set of all such locations is called 4 dimensional space, or, colloquially,… …   Wikipedia

• Timeline of algebra and geometry — A timeline of algebra and geometryBefore 1000 BC* ca. 2000 BC Scotland, Carved Stone Balls exhibit a variety of symmetries including all of the symmetries of Platonic solids. * 1800 BC Moscow Mathematical Papyrus, findings volume of a frustum *… …   Wikipedia

• Timeline of mathematics — A timeline of pure and applied mathematics history. Contents 1 Before 1000 BC 2 1st millennium BC 3 1st millennium AD 4 1000–1500 …   Wikipedia

• graph theory — Math. the branch of mathematics dealing with linear graphs. [1965 70] * * * Mathematical theory of networks. A graph consists of nodes (also called points or vertices) and edges (lines) connecting certain pairs of nodes. An edge that connects a… …   Universalium