Hauv kev lej, tshwj xeeb tshaj yog topology, homeomorphism hauv zos yog qhov ua haujlwm ntawm qhov chaw topological uas, intuitively, khaws cov qauv hauv zos. Yog tias f: X / rau Y yog ib qho homeomorphism hauv zos, X tau hais tias yog qhov chaw étale tshaj Y. Hauv zos homeomorphisms yog siv rau hauv kev kawm ntawm sheaves.
Puas yog homeomorphism hauv zos yog qhib daim ntawv qhia?
Properties. Txhua qhov homeomorphism hauv zos yog daim ntawv qhia txuas ntxiv thiab qhib. Yog li ntawd, ib qho homeomorphism hauv zos bijective yog qhov homeomorphism.
Qhov txawv ntawm homomorphism thiab homeomorphism yog dab tsi?
Raws lub npe qhov txawv ntawm homomorphism thiab homeomorphism. yog tias homomorphism yog (algebra) ib daim ntawv qhia kev khaws cia ntawm ob lub algebraic cov qauv, xws li pab pawg, rings, lossis vector qhov chaw thaum homeomorphism yog (topology) ib qho kev sib txuas ntxiv ntawm ib qho chaw topological mus rau lwm tus, nrog kev hloov pauv tsis tu ncua.
Koj ua li cas kuaj homeomorphism?
Yog x thiab y yog topologically sib npaug , muaj nuj nqi h: x → y xws li h yog txuas ntxiv, h yog mus rau (txhua qhov taw tes ntawm y sib raug rau ib qho taw tes. ntawm x), h yog ib-rau-ib, thiab inverse function, h−1, yog tas mus li. Yog li h hu ua homeomorphism.
Puas yog homeomorphism yog Diffeomorphism?
Rau qhov diffeomorphism, f thiab nws cov inverse yuav tsum sib txawv; rau homeomorphism, f thiab nws cov inverse xav tau tsuas yog txuas mus ntxiv. Txhua qhov diffeomorphism yog homeomorphism, tab sis tsis yog txhua tushomeomorphism yog diffeomorphism. f: M → N yog hu ua diffeomorphism yog tias, hauv cov kab kos ua ke, nws txaus siab rau qhov txhais saum toj no.
