Txhua txoj kev kaw hauv ib lub square thiab hauv ib lub voos xwmfab yog tib yam li tus taw tes, yog li lub voos xwmfab, ib lub xwmfab thiab ib qho taw tes yog tib hom homotopy.
Lub ntsiab lus ntawm homotopy yog dab tsi?
Nyob rau hauv topology, ib ceg ntawm kev ua lej, ob txoj haujlwm txuas ntxiv los ntawm ib qho chaw topological mus rau lwm qhov yog hu ua homotopic (los ntawm Greek ὁμός homós "zoo ib yam, zoo ib yam" thiab τόπος tópos "chaw") yog ib tau yuav "nruam deformed" mus rau lwm qhov, xws li deformation hu ua homotopy ntawm ob lub luag haujlwm.
cov chav kawm homotopy yog dab tsi?
homotopy theory
geometric region hu ua homotopy class. Cov txheej txheem ntawm tag nrho cov chav kawm no tuaj yeem muab cov qauv algebraic hu ua ib pawg, cov pab pawg hauv cheeb tsam, nws cov qauv sib txawv raws li hom cheeb tsam.
Koj pom homotopy li cas?
A homotopy ntawm f0 rau f1 yog ib map h: X × I → Y (nruam, tau kawg) xws li h(x, 0)=f0(x) thiab f(x, 1)=f1(x). Peb hais tias f0 thiab f1 yog homotopic, thiab hais tias h yog homotopy ntawm lawv. Qhov kev sib raug zoo no yog qhia los ntawm f0 ≃ f1. Homotopy yog qhov sib npaug sib npaug ntawm daim duab qhia chaw ntawm X rau Y.
Dab tsi yog qhov txawv ntawm homology thiab homotopy?
In topology|lang=en cov ntsiab lus qhov txawv ntawm homotopy thiab homology. yog hais tias homotopy yog (topology) ib qho txheej txheem ntawm pab pawg cuam tshuam rau qhov chaw topologicalthaum homology yog (topology) txoj kev xav sib koom ua ke ntawm pawg rau txhua qhov chaw topological.
