 euclidean spaces yokka upasamiti compact ani chupichadaniki saripaye remdu lakshanaalanu sangrahinchandi .  yea lakshanaalanu bullett jaabitaalo pradarsinchandi .
 sadarana stayini batti compact ‌ ness yokka vividha nirvachanalu vartinchavachhu .  mukhyamgaa euclidean spaces yokka upasamiti moosiveyabadi mariyu sarihaddulugaa vunte dhaanini compact antaruu .  idi bolzano - weir ‌ strass siddhaantam dwara ,  sett nundi edaina anantamaina srenini sett ‌ loni ooka binduvuku kalustundi ani suchisthundi .  sequential compact ‌ ness mariyu limit paayint compact ‌ ness vento vividha samaanamaina compact ‌ ness bhaavanalanu sadarana metrik spaces ‌ lalo abhivruddhi cheyavachu .

 deeniki viruddhamgaa ,  compact ‌ ness yokka vibhinna bhaavanalu sadarana topological spaces ‌ lalo samaanamgaa undavu mariyu compact ‌ ness yokka athantha upayogakaramaina Bodh  -  vaasthavaaniki bicampact ‌ ness ani pilustharu  -  open sett ‌ lato koodina cover ‌ lanu upayoginchi nirvachinchabadindi  ( crinda open cover definition chudandi ).  euclidean spaces yokka clogead mariyu bounded upasamitula choose yea rakamaina compact ‌ ness ‌ nu hean - borel siddhaantam antaruu .  compact ‌ ness ,  yea paddhatilo nirvachinchabadinappudu ,  tarachugaa sthaanikamgaa telisina samaachaaraanni teesukoovadaaniki anumatistundi  -  sdhalam yokka prathi bindhuvu yokka parisaraallo  -  mariyu antariksham antataa prapanchavyaapthamgaa unna samaacharaaniki dhaanini vistarimchadaaniki .  yea drugvishayaaniki ooka udaaharanha derichlet yokka siddhaantam ,  dheenini modhata hean vartimpajesaaru ,  compact viraamampai nirantara function ekareetigaa nirantharangaa umtumdi ;  ikda ,  konasaagimpu anede function yokka stanika aasti ,  mariyu yekareeti konasaagimpu sambandhitha prapancha aasti .
 hean - borel siddhaantam prakaaram euclidean spaces yokka upasamiti compact ani chupichadaniki krindhi lakshanhaalu saripotayi :
-  sett moosiveyabadindi 
-  sett parimitamaimdi 