:: TSP_1 semantic presentation
:: deftheorem Def1 defines SubSpace TSP_1:def 1 :
theorem Th1: :: TSP_1:1
canceled;
theorem Th2: :: TSP_1:2
:: deftheorem Def2 defines SubSpace TSP_1:def 2 :
theorem Th3: :: TSP_1:3
canceled;
theorem Th4: :: TSP_1:4
:: deftheorem Def3 defines T_0 TSP_1:def 3 :
:: deftheorem Def4 defines T_0 TSP_1:def 4 :
Lemma54:
for X being non empty non trivial anti-discrete TopStruct holds not X is T_0
Lemma56:
for X being non empty TopSpace
for x being Point of X holds x in Cl {x}
Lemma57:
for X being non empty TopSpace
for A, B being Subset of X st B c= Cl A holds
Cl B c= Cl A
by TOPS_1:31;
:: deftheorem Def5 defines T_0 TSP_1:def 5 :
:: deftheorem Def6 defines T_0 TSP_1:def 6 :
:: deftheorem Def7 defines T_0 TSP_1:def 7 :
:: deftheorem Def8 defines T_0 TSP_1:def 8 :
:: deftheorem Def9 defines T_0 TSP_1:def 9 :
theorem Th5: :: TSP_1:5
theorem Th6: :: TSP_1:6
theorem Th7: :: TSP_1:7
theorem Th8: :: TSP_1:8
theorem Th9: :: TSP_1:9
theorem Th10: :: TSP_1:10
theorem Th11: :: TSP_1:11
theorem Th12: :: TSP_1:12
:: deftheorem Def10 defines T_0 TSP_1:def 10 :
:: deftheorem Def11 defines T_0 TSP_1:def 11 :
:: deftheorem Def12 defines T_0 TSP_1:def 12 :
theorem Th13: :: TSP_1:13
theorem Th14: :: TSP_1:14
:: deftheorem Def13 defines T_0 TSP_1:def 13 :
:: deftheorem Def14 defines T_0 TSP_1:def 14 :
theorem Th15: :: TSP_1:15
theorem Th16: :: TSP_1:16
theorem Th17: :: TSP_1:17
theorem Th18: :: TSP_1:18
theorem Th19: :: TSP_1:19
theorem Th20: :: TSP_1:20
theorem Th21: :: TSP_1:21