:: Dyadic Numbers and $T_4$ Topological Spaces
:: by J\'ozef Bia\las and Yatsuka Nakamura
::
:: Received July 29, 1995
:: Copyright (c) 1995 Association of Mizar Users
:: deftheorem URYSOHN1:def 1 :
canceled;
:: deftheorem URYSOHN1:def 2 :
canceled;
:: deftheorem Def3 defines dyadic URYSOHN1:def 3 :
:: deftheorem Def4 defines DYADIC URYSOHN1:def 4 :
:: deftheorem defines DOM URYSOHN1:def 5 :
theorem :: URYSOHN1:1
canceled;
theorem :: URYSOHN1:2
canceled;
theorem :: URYSOHN1:3
canceled;
theorem :: URYSOHN1:4
canceled;
theorem Th5: :: URYSOHN1:5
theorem Th6: :: URYSOHN1:6
theorem :: URYSOHN1:7
theorem :: URYSOHN1:8
canceled;
theorem Th9: :: URYSOHN1:9
:: deftheorem Def6 defines dyad URYSOHN1:def 6 :
theorem :: URYSOHN1:10
theorem Th11: :: URYSOHN1:11
theorem Th12: :: URYSOHN1:12
theorem Th13: :: URYSOHN1:13
theorem Th14: :: URYSOHN1:14
theorem Th15: :: URYSOHN1:15
:: deftheorem Def7 defines axis URYSOHN1:def 7 :
theorem Th16: :: URYSOHN1:16
theorem :: URYSOHN1:17
theorem Th18: :: URYSOHN1:18
theorem :: URYSOHN1:19
canceled;
theorem Th20: :: URYSOHN1:20
theorem Th21: :: URYSOHN1:21
theorem Th22: :: URYSOHN1:22
theorem Th23: :: URYSOHN1:23
:: deftheorem defines Nbhd URYSOHN1:def 8 :
theorem Th24: :: URYSOHN1:24
theorem :: URYSOHN1:25
canceled;
theorem :: URYSOHN1:26
:: deftheorem Def9 defines T_1 URYSOHN1:def 9 :
theorem Th27: :: URYSOHN1:27
theorem Th28: :: URYSOHN1:28
theorem :: URYSOHN1:29
theorem :: URYSOHN1:30
theorem :: URYSOHN1:31
:: deftheorem Def10 defines Between URYSOHN1:def 10 :
theorem :: URYSOHN1:32