theorem Th27:
for
n being
Nat for
P being
Subset of
(TOP-REAL n) for
w1,
w2,
w3,
w4,
w5,
w6,
w7 being
Point of
(TOP-REAL n) st
w1 in P &
w2 in P &
w3 in P &
w4 in P &
w5 in P &
w6 in P &
w7 in P &
LSeg (
w1,
w2)
c= P &
LSeg (
w2,
w3)
c= P &
LSeg (
w3,
w4)
c= P &
LSeg (
w4,
w5)
c= P &
LSeg (
w5,
w6)
c= P &
LSeg (
w6,
w7)
c= P holds
ex
h being
Function of
I[01],
((TOP-REAL n) | P) st
(
h is
continuous &
w1 = h . 0 &
w7 = h . 1 )