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鏄犲皠鐨勫畾缇╋紝閫ｇ簩(x霉)鏄犲皠鐨勪竴浜涚瓑鍍瑰畾缇�銆�
绗簩閮ㄥ垎鎷撴挷绌洪枔閬嬬畻
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鑰冩牳瑕佹眰锛�
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鍟嗘槧灏勩€佸晢绌洪枔銆侀枊锛堥枆锛夋槧灏勭殑瀹氱京瑕佹眰璀樿锛�
锛�2锛夌悊瑙ｅ瓙绌洪枔鎷撴挷銆佹湁闄愮⿳鎷撴挷鍜屽晢鎷撴挷鑸囧師鎷撴挷绌洪枔鎷撴挷鐨�
闂滅郴锛�
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鑸囨€ц唱(zh矛)锛�
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绗笁閮ㄥ垎鎷撴挷绌洪枔鎬ц唱(zh矛)
1.閫ｉ€氭€�
鑰冩牳鍏�(n猫i)瀹癸細閫ｉ€氭€х殑鎳夌敤閫ｉ€氬垎鏀眬閮ㄩ€ｉ€氱┖闁撻亾璺€ｉ€氱┖闁撻亾
璺€ｉ€氬垎鏀�
鑰冩牳瑕佹眰锛�
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閫ｉ€氬瓙闆�銆侀€ｉ€氬垎鏀�銆佸眬閮ㄩ€ｉ€氱┖闁�銆侀亾璺€ｉ€氱┖闁撶瓑姒傚康瑕佹眰璀樿锛�
锛�2锛夌悊瑙ｉ€ｉ€氬瓙闆嗭紝閫ｇ簩(x霉)鏄犲皠淇濇寔涓嶈畩鐨勬€ц唱(zh矛)锛�
锛�3锛夋帉鎻￠€ｉ€氱┖闁�銆侀亾璺€ｉ€氱┖闁�銆佸眬閮ㄩ€ｉ€氱┖闁撱€佹湁闄愬彲绌嶆€�
璩�(zh矛)銆侀€ｉ€氬瓙闆�銆侀€ｉ€氬垎鏀€佸眬閮ㄩ€ｉ€氱┖闁�銆侀亾璺€ｉ€氱┖闁撶殑鎬ц唱(zh矛)锛屾帉鎻�
閫ｉ€氱┖闁�銆侀亾璺€ｉ€氱┖闁�銆佸眬閮ㄩ€ｉ€氱┖闁撳垽瀹氭柟娉�锛�
锛�4锛夋渻鎳夌敤閫ｉ€氱┖闁撱€侀亾璺€ｉ€氱┖闁�銆佸眬閮ㄩ€ｉ€氱┖闁撱€佹湁闄愬彲绌�
鎬ц唱(zh矛)銆侀€ｉ€氬瓙闆�銆侀€ｉ€氬垎鏀�銆佸眬閮ㄩ€ｉ€氱┖闁�銆侀亾璺€ｉ€氱┖闁撶殑鎬ц唱(zh矛)銆�
2.鍙暩(sh霉)鎬�
鑰冩牳鍏�(n猫i)瀹癸細绗竴鍙暩(sh霉)鎬у叕鐞嗙浜屽彲鏁�(sh霉)鎬у叕鐞嗗彲鍒嗙┖闁� Lindeloff 绌�
闁�
鑰冩牳瑕佹眰锛�
锛�1锛夊皪鍙暩(sh霉)鎬у叕鐞�銆佸彲鍒嗙┖闁撱€丩indeloff 绌洪枔绛夋蹇佃姹傝瓨瑷�锛�
锛�2锛夌悊瑙� A2 绌洪枔鍜� A1 绌洪枔鐨勯棞绯伙紝鍙暩(sh霉)鎬у叕鐞嗙殑鍙伜鍌虫€ц唱(zh矛)
鍙婃湁闄愬彲绌嶆€ц唱(zh矛)锛�
锛�3锛夋帉鎻″彲鏁�(sh霉)鎬у叕鐞嗐€佸彲鍒嗙┖闁�銆丩indeloff 绌洪枔鐨勬€ц唱(zh矛)锛�
锛�4锛夋渻鎳夌敤鍙暩(sh霉)鎬у叕鐞�銆佸彲鍒嗙┖闁�銆丩indeloff 绌洪枔鐨勬€ц唱(zh矛)銆�
3.鍒嗛洟鎬�
鑰冩牳鍏�(n猫i)瀹癸細T0銆乀1銆丠ausdorff 绌洪枔姝ｅ墖绌洪枔姝ｈ(gu墨)绌洪枔 T3銆乀4
绌洪枔 Urysohn 寮曠悊 Tietze 鎿村嫉瀹氱悊瀹屽叏姝ｅ墖绌洪枔 Tychonoff 绌洪枔鍒嗛洟
鎬у叕鐞嗚垏瀛愮┖闁撴湁闄愮⿳绌洪枔鍜屽晢绌洪枔鍙害閲忓寲绌洪枔
鑰冩牳瑕佹眰锛�
锛�1锛夊皪 T0銆乀1銆乀2銆乀3銆乀4銆佹鍓�銆佹瑕�(gu墨)銆佸畬鍏ㄦ鍓囩┖闁撱€�
Tychonoff 绌洪枔绛夋蹇佃姹傝瓨瑷樿В锛�
锛�2锛夌悊瑙� Urysohn 寮曠悊锛孴ietze 鎿村嫉瀹氱悊銆乁rysohn 宓屽叆瀹氱悊鐨�
鍏�(n猫i)瀹瑰強璀夋槑鏂规硶锛�
锛�3锛夋帉鎻� T0銆乀1銆佹鍓�銆佹瑕�(gu墨)銆佸畬鍏ㄦ鍓�銆乀ychonoff 绌洪枔鐨�
鎬ц唱(zh矛)锛�
锛�4锛夋渻鎳夌敤 T0銆乀1銆佹鍓�銆佹瑕�(gu墨)銆佸畬鍏ㄦ鍓�銆乀ychonoff 绌洪枔
鐨勬€ц唱(zh矛)銆�
4.绶婅嚧鎬�
鑰冩牳鍏�(n猫i)瀹癸細绶婅嚧绌洪枔绶婅嚧鎬ц垏鍒嗛洟鎬у叕鐞嗗咕绋穵鑷存€т互鍙婂叾闁撻棞
绯诲害閲忕┖闁撲腑鐨勭穵鑷存€у眬閮ㄧ穵鑷寸┖闁�
鑰冩牳瑕佹眰锛�
锛�1锛夊皪绶婅嚧銆佸彲鏁�(sh霉)绶婅嚧銆佸垪绶�銆佸簭鍒楃穵鑷�銆佸眬閮ㄧ穵鑷寸┖闁撶瓑姒傚康
瑕佹眰璀樿锛�
锛�2锛夌悊瑙ｇ穵鑷�銆佸彲鏁�(sh霉)绶婅嚧銆佸垪绶�銆佸簭鍒楃穵鑷寸殑鎬ц唱(zh矛)鍙婂叾鐩镐簰闂滅郴锛�
锛�3锛夋帉鎻＄穵鑷�銆佺穵鑷村瓙闆嗐€佸彲鏁�(sh霉)绶婅嚧銆佸垪绶娿€佸簭鍒楃穵鑷寸殑鎬ц唱(zh矛)锛�
绶婅嚧绌洪枔銆佺穵鑷村瓙闆嗐€佸彲鏁�(sh霉)绶婅嚧銆佸垪绶�銆佸簭鍒楃穵鑷寸┖闁撶殑鍒ゅ垾鏂规硶锛岀穵
鑷存€у拰鍒嗛洟鎬у叕鐞嗙殑闂滅郴锛�
锛�4锛夋渻鎳夌敤绶婅嚧銆佸彲鏁�(sh霉)绶婅嚧銆佸垪绶�銆佸簭鍒楃穵鑷寸殑鎬ц唱(zh矛)銆�
涓�銆侀鍨嬬祼(ji茅)妲�(g貌u)
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鍏嶈铂鑱叉槑锛氭湰鏂囩郴杞�(zhu菐n)杓夎嚜缍�(w菐ng)绲�锛屽鏈変镜鐘�锛岃珛鑱�(li谩n)绯绘垜鍊戠珛鍗冲埅闄�锛屽彟锛氭湰鏂囧儏浠ｈ〃浣滆€呭€嬩汉瑙€榛�锛岃垏鏈恫(w菐ng)绔欑劇闂�銆傚叾鍘熷壍(chu脿ng)鎬т互鍙婃枃涓櫝杩版枃瀛楀拰鍏�(n猫i)瀹规湭缍�(j墨ng)鏈珯璀夊锛屽皪鏈枃浠ュ強鍏朵腑鍏ㄩ儴鎴栬€呴儴鍒嗗収(n猫i)瀹�銆佹枃瀛楃殑鐪熷鎬�銆佸畬鏁存€�銆佸強鏅傛€ф湰绔欎笉浣滀换浣曚繚璀夋垨鎵胯锛岃珛璁€鑰呭儏浣滃弮鑰�锛屽苟璜嬭嚜琛屾牳瀵︾浉闂滃収(n猫i)瀹�銆�
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