begin
:: deftheorem Def1 defines a_neighborhood CONNSP_2:def 1 :
:: deftheorem Def2 defines a_neighborhood CONNSP_2:def 2 :
theorem
canceled;
theorem
canceled;
theorem
theorem
theorem Th5:
theorem Th6:
theorem Th7:
theorem Th8:
theorem
theorem
theorem Th11:
Lm1:
for X being non empty TopSpace
for X1 being SubSpace of X
for A being Subset of X
for A1 being Subset of X1 st A = A1 holds
(Int A) /\ ([#] X1) c= Int A1
theorem Th12:
theorem Th13:
theorem
:: deftheorem Def3 defines is_locally_connected_in CONNSP_2:def 3 :
:: deftheorem Def4 defines locally_connected CONNSP_2:def 4 :
:: deftheorem Def5 defines is_locally_connected_in CONNSP_2:def 5 :
:: deftheorem Def6 defines locally_connected CONNSP_2:def 6 :
theorem
canceled;
theorem
canceled;
theorem
canceled;
theorem
canceled;
theorem Th19:
theorem Th20:
theorem Th21:
theorem Th22:
theorem Th23:
theorem Th24:
theorem
theorem Th26:
theorem
theorem Th28:
:: deftheorem Def7 defines qComponent_of CONNSP_2:def 7 :
theorem
canceled;
theorem
theorem
theorem
theorem
theorem
theorem
theorem