Relative Homotopie von Wegen
Es sei
I
=
[
0
,
1
]
{\displaystyle {}I=[0,1]}
γ
1
,
γ
2
:
I
→
X
{\displaystyle {}\gamma _{1},\gamma _{2}\colon I\rightarrow X}
stetige Wege
in einen
topologischen Raum
X
{\displaystyle {}X}
γ
1
(
0
)
=
γ
2
(
0
)
{\displaystyle {}\gamma _{1}(0)=\gamma _{2}(0)}
γ
1
(
1
)
=
γ
2
(
1
)
{\displaystyle {}\gamma _{1}(1)=\gamma _{2}(1)}
Homotopie relativ
{
0
,
1
}
{\displaystyle {}\{0,1\}}
γ
1
{\displaystyle {}\gamma _{1}}
γ
2
{\displaystyle {}\gamma _{2}}
H
:
I
×
I
⟶
X
,
{\displaystyle H\colon I\times I\longrightarrow X,}
die die folgenden Eigenschaften erfüllt.
H
(
s
,
0
)
=
γ
1
(
s
)
{\displaystyle {}H(s,0)=\gamma _{1}(s)}
s
∈
I
{\displaystyle {}s\in I}
H
(
s
,
1
)
=
γ
2
(
s
)
{\displaystyle {}H(s,1)=\gamma _{2}(s)}
s
∈
I
{\displaystyle {}s\in I}
H
(
0
,
t
)
=
γ
1
(
0
)
{\displaystyle {}H(0,t)=\gamma _{1}(0)}
t
∈
I
{\displaystyle {}t\in I}
H
(
1
,
t
)
=
γ
1
(
1
)
{\displaystyle {}H(1,t)=\gamma _{1}(1)}
t
∈
I
{\displaystyle {}t\in I}
![{\displaystyle {}I=[0,1]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f6e907ddfe40276b89fefc275def3fc51455de60)
