
atyant disconnect keleli jaaga

ganitat, atyant disconnect keleli jaaga hii eka topological jaaga aahe jyamadhye pratyek khulya sanchala bund karane khule asate. (jaree bahutek shabdakoshanmadhye 'atyant' haah shabd disat nasla, taree 'atyant disconnect' haah shabd barobar aahe aanee kadhikadhi spelchekarsdware 'atyant disconnect' assa homophone mhanoon chukun samajala jaato.)
atyant vichchhedit jaaga jee sankshipt aanee bhoo-aachchadan dekhil asate teela kadhikadhi stonen space mhanatat. hii dagadi jagesarkhi nahee, jee purnapane disconnect keleli compact hosdorf jaaga aahe. pratyek dagadi jaaga hii eka dagadi jaaga asate, parantu tyaulat nahee. dagadi jaaga aanee booliyan algebra yanchyatil dwaitatemadhye, dagadi jaaga sampoorn booliyan algebrashi sambandhit aahet. 
pratham gananiy, atyant disconnect keleli, sangrahanusarchi, housedorf jaaga swatantra asane aavashyak aahe. visheshtah, metrik jagansathi, atyant disconnect honyacha gunadharm (pratyek khulya sanchala bund karane khule asate) haah swatantra asanyachya (pratyek sanch khula asato) gunadharmanchya samatulya aahe.
samatulya varnane.
compact hasdorf spaceschya shrenitil projective objects agadi atyant disconnect kelelya compact hasdorf spaces aahet asey eka pramey mhanato. yaa vastusthiticha eka sopa purava yaa dware deela aahe.
jarr aanee keval jarr tee vegalya jagechya dagad-shikachya sankshiptatechi mage hatat asel tarach eka sankshipt hosdorf jaaga atyant disconnect kelee jaate.
anuprayog.
 atyant disconnect kelelya jaganchya babatit qamee karoon, eriz-markov-kakutani pratinidhitva pramey siddha karate, asha paristhitit pratinidhitva pramey prathamik madhyamandvare siddha kele jaau shakate.