theorem
Th45
:
:: JORDAN6:45
for
T
,
S
,
V
being non
empty
TopSpace
for
P1
being non
empty
Subset
of
S
for
P2
being
Subset
of
S
for
f
being
Function
of
T
,
(
S

P1
)
for
g
being
Function
of
(
S

P2
)
,
V
st
P1
c=
P2
&
f
is
continuous
&
g
is
continuous
holds
ex
h
being
Function
of
T
,
V
st
(
h
=
g
*
f
&
h
is
continuous
)