ekman-hilton dwait

bijganitiy topology aanee samarupata siddhant yaa ganiteey shakhanmadhye, ekman-hilton dwaitata tyachya sarvat moolbhut swarupat, vishisht sankalpanesathi dileli aakruti ghene aanee serve bananchi disha ulat karane samavisht aahe, agadi shreni siddhantat viruddha shrenichya kalpanesah. eka lakshaniy sakhol prakar assa yuktivad karato qee maryadechi duheri kalpana hii eka colimit aahe hii vastusthiti aaplyala samarupatesathi swayamsiddhi denyasathi samarupatesathi eyelenberg-steinroad swayamsiddhi badalanyas anumati dete. yala beno ekman aanee pieter hilton yanche naav denyat aale aahe.
charcha.
eka udaharan karingdware dile jaate, jeey aaplyala sangate qee konatyahi object sutrasathi _ 1, nakasha sootra _ 2 heey nakasha sootra _ 3 sarkhech aahe, jethe sootra _ 4 hii ghatankiy vastoo aahe, jee sootra _ 5 teey sootra _ 6 paryantchya serve nakashandware dilee gelee aahe. topological spaceschya babatit, jarr aapan sootra _ 5 laa ekak antaral mhanoon ghetale tarr heey sootra _ 8 aanee sootra _ 4 darmyan dwaitatekade netat, jeey nantar qamee kelele nilamban sootra _ 10, jeey sootra _ 11 chaa bhag aahe aanee loop space sootra _ 12, jeey sootra _ 13 chey upkshetra aahe, yanchyat dwaitata dete. heey nantar sanlagn sambandh sootra _ 14 kadey jaate, jeey varnapat abhyasas anumati dete, jeey cohomology siddhantanna janm dete.
aapan tantuncha aanee sahasanyugmancha thet sambandh dekhil thevu shakatoh eka tantumay sootra _ 15 heey samarupi uchalanyacha gunadharm asalyamule paribhashit kele jaate, jeey khaleel aakrutidvare darshavile jaate.
aanee sahasanyaman sootra _ 16 heey duheri samarupata vistar gunadharm asalelyadvare paribhashit kele jaate, jeey mageel aakrutiche duherikaran karoon darshavile jaateh
tantumay kinwa sahasanyojanashi sambandhit anukram pahatana vareel vichar dekhil lagoo hotat, tantumay sootra dilyapramane aaplyala kram midato.
aanee coffibration sootra dile tarr aaplyala kram midato
aanee adhik samanyatah, achook aanee sahabhinayit kathputalichya anukramanmadhil dvandva.
yamule aaplyala samarupata aanee samarupata yancha sambandh jodata yetoh aaplyala mahit aahe qee samarupata gut heey "aine"-kshetrapasun aaplya jageparyantchya nakashanche samarupata varg aahet, likhit sootra _ 21, aanee aaplyala mahit aahe qee yaa golamadhye ekach shunyetar (qamee) samarupata gut aahe. dusarikade, samarupata gut heey ekach shunyetar samarupata gatasah mokalya jagansathichya nakashanche samarupata varg aahet. heey eyelenberg-mclain space sootra _ 22 aanee sambandhadvare dile jaate. 
vareel anaupacharik sambandhanche aupcharikaran fuxchya dwaitatvadvare dile jaate.

