:: Uniform Continuity of Functions on Normed Complex Linear Spaces
:: by Noboru Endou
::
:: Received October 6, 2004
:: Copyright (c) 2004 Association of Mizar Users
:: deftheorem Def1 defines is_uniformly_continuous_on NCFCONT2:def 1 :
:: deftheorem Def2 defines is_uniformly_continuous_on NCFCONT2:def 2 :
:: deftheorem Def3 defines is_uniformly_continuous_on NCFCONT2:def 3 :
:: deftheorem Def4 defines is_uniformly_continuous_on NCFCONT2:def 4 :
:: deftheorem Def5 defines is_uniformly_continuous_on NCFCONT2:def 5 :
:: deftheorem Def6 defines is_uniformly_continuous_on NCFCONT2:def 6 :
theorem Th1: :: NCFCONT2:1
theorem Th2: :: NCFCONT2:2
theorem Th3: :: NCFCONT2:3
theorem :: NCFCONT2:4
theorem :: NCFCONT2:5
theorem :: NCFCONT2:6
theorem :: NCFCONT2:7
theorem :: NCFCONT2:8
theorem :: NCFCONT2:9
theorem Th10: :: NCFCONT2:10
theorem Th11: :: NCFCONT2:11
theorem Th12: :: NCFCONT2:12
theorem :: NCFCONT2:13
theorem :: NCFCONT2:14
theorem :: NCFCONT2:15
theorem :: NCFCONT2:16
theorem :: NCFCONT2:17
theorem :: NCFCONT2:18
theorem Th19: :: NCFCONT2:19
theorem Th20: :: NCFCONT2:20
theorem Th21: :: NCFCONT2:21
theorem :: NCFCONT2:22
theorem Th23: :: NCFCONT2:23
theorem :: NCFCONT2:24
theorem Th25: :: NCFCONT2:25
theorem Th26: :: NCFCONT2:26
theorem Th27: :: NCFCONT2:27
theorem :: NCFCONT2:28
theorem :: NCFCONT2:29
theorem :: NCFCONT2:30
theorem :: NCFCONT2:31
theorem :: NCFCONT2:32
theorem :: NCFCONT2:33
theorem :: NCFCONT2:34
theorem :: NCFCONT2:35
theorem :: NCFCONT2:36
theorem :: NCFCONT2:37
:: deftheorem Def7 defines contraction NCFCONT2:def 7 :
theorem :: NCFCONT2:38
theorem :: NCFCONT2:39
Lm1:
for X being ComplexNormSpace
for x, y, z being Point of X
for e being Real st e > 0 & ||.(x - z).|| < e / 2 & ||.(z - y).|| < e / 2 holds
||.(x - y).|| < e
Lm2:
for X being ComplexNormSpace
for x, y, z being Point of X
for e being Real st e > 0 & ||.(x - z).|| < e / 2 & ||.(y - z).|| < e / 2 holds
||.(x - y).|| < e
Lm3:
for X being ComplexNormSpace
for x being Point of X st ( for e being Real st e > 0 holds
||.x.|| < e ) holds
x = 0. X
Lm4:
for X being ComplexNormSpace
for x, y being Point of X st ( for e being Real st e > 0 holds
||.(x - y).|| < e ) holds
x = y
theorem Th40: :: NCFCONT2:40
theorem :: NCFCONT2:41