Solid Klein bottle
Three-dimensional topological space
In mathematics, a solid Klein bottle is a three-dimensional topological space (a 3-manifold) whose boundary is the Klein bottle.[1]
It is homeomorphic to the quotient space obtained by gluing the top disk of a cylinder to the bottom disk by a reflection across a diameter of the disk.
Alternatively, one can visualize the solid Klein bottle as the trivial product , of the möbius strip and an interval . In this model one can see that the core central curve at 1/2 has a regular neighborhood which is again a trivial cartesian product: and whose boundary is a Klein bottle.
References
- ^ Carter, J. Scott (1995), How Surfaces Intersect in Space: An Introduction to Topology, K & E series on knots and everything, vol. 2, World Scientific, p. 169, ISBN 9789810220662.
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Manifolds (Glossary)
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- in Lie theory
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manifolds
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