Ib tus sau npe hu ua yooj yim txuas yog tias muaj ob qhov nkhaus nrog tib lub ntsiab lus kawg yog homotopic. Los yog sib npaug, txhua qhov nkhaus kaw yog homotopic rau qhov taw tes (uas yog hais, nws homotopic mus rau qhov nkhaus tas li).
Kev sib txuas yooj yim txhais tau li cas?
Nws yog ib qho kev ua si classic thiab theem pib hauv topology los qhia tias, yog qhov chaw sib txuas, ces nws txuas. Yog li, yog tias qhov chaw sib txuas yooj yim, ces nws txuas nrog.
Puas yog qhov chaw sib txuas yooj yim cog lus tau?
Definition: Ib qho chaw sib txuas yooj yim yog qhov chaw txuas nrog X uas nws pab pawg neeg hlwb II. (X) yog pab pawg tsis tseem ceeb uas tsuas yog muaj cov cim qhia txog tus kheej xwb. … Ib qhov chaw X yog cog lus yog tias muaj qhov taw tes xo hauv X uas X tau cog lus rau Xo.
Dab tsi yog qhov sib txuas yooj yim?
A nto (ob-seem topological manifold) tsuas yog txuas yog tias nws txuas nrog thiab nws cov genus(tus naj npawb ntawm tes ntawm qhov chaw) yog 0. A universal npog ntawm ib qho (tsim) qhov chaw yog ib qho yooj yim txuas qhov chaw uas maps rau. ntawm daim ntawv qhia npog.
Puas yog R3 txuas yooj yim?
(5) R3 rho tawm ib kab segment yooj yim txuas. Qhov no muaj feem xyuam rau topology, uas cuam tshuam nrog kev faib tawm ntawm cov khoom geometric mus rau deforming lawv zoo li cov roj hmab (yog li koj tuaj yeem ncab tab sis tsis tsim kua muag). Qhov saum npoo ntawm tus kheej kheej yog qhov sib txawv ntawm qhov saum npoo ntawm lub torus.
