theorem
for
p1,
p2,
p3,
p4 being
Point of
(TOP-REAL 2) for
C0 being
Subset of
(TOP-REAL 2) st
C0 = { p where p is Point of (TOP-REAL 2) : |.p.| >= 1 } &
|.p1.| = 1 &
|.p2.| = 1 &
|.p3.| = 1 &
|.p4.| = 1 & ex
h being
Function of
(TOP-REAL 2),
(TOP-REAL 2) st
(
h is
being_homeomorphism &
h .: C0 c= C0 &
h . p1 = |[(- 1),0]| &
h . p2 = |[0,1]| &
h . p3 = |[1,0]| &
h . p4 = |[0,(- 1)]| ) holds
for
f,
g being
Function of
I[01],
(TOP-REAL 2) st
f is
continuous &
f is
one-to-one &
g is
continuous &
g is
one-to-one &
f . 0 = p1 &
f . 1
= p3 &
g . 0 = p4 &
g . 1
= p2 &
rng f c= C0 &
rng g c= C0 holds
rng f meets rng g