
ralph phoox

oru american ganithashaasthranjanaayirunnu ralph hartsler phoox (march 24,1913-desember 23,1973). prinsettan sarvakalaashaalayile professor enna nilayil, "deferential topology suvarnna kaalaghatta" thilekk sambhavana nalkia palareyum addeham padippikkukayum upadeshikkukayum cheythu, koodaathe nottu sidhaanthathinte aadhunikavalkkaranathilum pradhana streamingle addeham oru pradhana punk vahichu.
jeevacharitram.
philadelphiyayile leafson kansarvettari oof myusikkil piano padikkumbol rund varshatholam swarthmore collegil chernnu. johns hopkins sarvakalashaalayil ninnu birudaananthara birudavum 1939ll prinsettan sarvakalashaalayil ninnu phd birudavum nedi. solomon lefshetts samvidaanam cheytha "lasternik-snirelman vibhaagathekkurichulla" doctoral prabandham. (pinneedulla varshangalil addeham lasternik-sneerelman vibhaagathekkurichulla ellah arivum nishedhikkukayum theerchayaayum eee vishayathil veendum orikkalum prasidheekarikkaathirikkum cheythu.) joonn milnor, joonn staalings, francisco gonsaalas-akuna, gillermo torres-dias, baari masoor ennivarulppede 21 doctoral prabandhangal addeham samvidaanam cheyyukayum kenn percoyude biruda prabandhathinu melnottam vahikkukayum cheythu.
1950ll masaachyusetsile kembridjil nadanna ganithashaasthranjarude anthaaraashtra kongrasil addeham shanikkappetta prabhashakanaayirunnu. addehathinte ganithashaasthra sambhaavanakalil phoox "enn"-nottsinte niram, phoox-artin arck, free deferential calculus enniva ulppedunnu. function speysukalile compact-ooppan topology homotopy sidhaanthathinu prathyekichum anuyojyamaanennu addeham thiricharinju.
karsanamaaya ganithashaasthra sambhaavanakalkk purame, nottu sidhaanthathinu niravadhi adisthaana vaakyangal avatharippikkunnathil addeham utharavaadiyaayirunnu "slies nottu", "riban nottu", "seifert sarkkil" ennee padangal ellaam addehathinte peril aadyamaayi achadikku prathyakshappedunnu, koodaathe addeham "seifert uparithalam" enna padaprayogam janapriyamakki (addeham avatharippichillenkil).
prinsettanilum instittyoott phoor advanced stadiyilum goo geyim kalikkunnathu addeham janapriyamakki.