
duns thoppi (topology)

topologyil, oru soolid triangle eduthu moonnu vashangalum orumichu ottichu oru vashathinte ooriyanteshan vipareethamaakki roopappedunna oru compact topological spessaanu duns haatt. ethirdishayil rund vashangalum ottichaal duns thoppi pole oru koonn labikkum, ennaal moonnaam vashathinte ottikkunnath thoppiyude aditharaye adiyil cherunna oru variyode thirichariyaan kaaranamaakunnu. 
peru.
iii enna peraanu kaaranam. sii. clossed yoonit edavelayil cartician uthppannam eduthathinu sesham eathenkilum kararulla 2-complexes (duns thoppi polullava) thakarkkaavunnathaanennu seeman nireekshichu. eee nireekshanam seeman anumaanam ennariyappedukayum poincare anumaanam soochippikkaan seeman kaanikkukayum cheythu.
swathukkal.
duns thoppi kararullathaanu, pakshe polikkaan kazhiyilla. duns thoppi 3-panthil ulchernnuvennum 3-panthinte vaikalyam duns thoppiyil pinvaangunnuvennum shradhikkunnathiloode karar eluppathil kaanaan kazhiyum. pakaram, 2-sellinte athirthi vrithathilekku ottichu labhikkuna sii. dablyu-complexaanu duns thoppi ennathu shradhikkuka. gluying mapp vrithathile aidantitti maappin homotopic aanu, athinaal complexes diskinu thulyamaaya homotopy. ithinu vipareethamaayi, ithinu swathanthramaaya oru mukham illaathathinaal ithu thakarkkanavilla.