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Invariance of Domain
Invariance of Domain
📜
The statement of the theorem
If
U
U
U
is an open subset of
R
n
\mathbb{R}^n
R
n
and
f
:
U
→
R
n
f: U \to \mathbb{R}^n
f
:
U
→
R
n
is an injective continuous map, then
V
=
f
(
U
)
V=f(U)
V
=
f
(
U
)
is open and
f
f
f
is a homeomorphism between
U
U
U
and
V
V
V
.
Source: Wikipedia