|
|
| Line 1: |
Line 1: |
| In [[mathematics]], a '''solid Klein bottle''' is a [[3-manifold]] (with boundary) [[homeomorphism|homeomorphic]] to the [[quotient space]] obtained by gluing the top of <math>\scriptstyle D^2 \times I</math> (cylinder) to the bottom by a reflection, i.e. the point <math>\scriptstyle (x,0)\,</math> is identified with <math>\scriptstyle (r(x), 1)\,</math> where <math>\scriptstyle r\,</math> is reflection of the disc <math>\scriptstyle D^2\,</math> across a diameter.
| | The author's title is Andera and she believes it seems fairly great. North Carolina is exactly where we've been residing for years and will by no means transfer. To climb is some thing she would by no means give up. Office supervising is what she does for a living.<br><br>Also visit my web page - [http://www.publicpledge.com/blogs/post/7034 tarot readings] |
| [[File:Moxi003.JPG|120px|thumb|right|Mö x I: the circle of black points marks an absolute [[deformation retract]] of this space, and any regular neighbourhood of it has again boundary as a Klein bottle, so Mö x I is an onion of Klein bottles]]
| |
|
| |
| Note the boundary of the solid Klein bottle is a [[Klein bottle]].
| |
| | |
| Alternatively, one can visualize the solid Klein bottle as the [[I-bundle|trivial product]] <math>\scriptstyle M\ddot{o}\times I</math>, of the [[möbius strip]] and an interval <math>\scriptstyle I=[0,1]</math>. 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]]: <math>\scriptstyle M\ddot{o}\times[\frac{1}{2}-\varepsilon,\frac{1}{2}+\varepsilon]</math> and whose boundary is a Klein bottle as previously noticed
| |
| | |
| [[Category:3-manifolds]]
| |
| | |
| | |
| {{topology-stub}}
| |
Latest revision as of 15:36, 26 November 2014
The author's title is Andera and she believes it seems fairly great. North Carolina is exactly where we've been residing for years and will by no means transfer. To climb is some thing she would by no means give up. Office supervising is what she does for a living.
Also visit my web page - tarot readings