Warren Garza
07/07/2024 · Middle School
1. \( x:\{a, b\} T_{x}: \) Topologia discreta \( y:\{1,2,3\} T_{y}: \) Topologia Trivial. \( f: x \rightarrow y \quad g: x \rightarrow y \) \( f(a)=1 \quad g(a)=2 \) \( f(b)=2 \quad g(b)=3 \) Hallar la homotopía entre \( f y g \)
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Se define una homotopía \( H \) entre \( f \) y \( g \) de la siguiente manera:
\[
H(a, t) =
\begin{cases}
1 & \text{si } t = 0 \\
2 & \text{si } 0 < t < 1 \\
3 & \text{si } t = 1
\end{cases}
\]
\[
H(b, t) =
\begin{cases}
2 & \text{si } t = 0 \\
2 & \text{si } 0 < t < 1 \\
3 & \text{si } t = 1
\end{cases}
\]
Esta homotopía conecta \( f \) y \( g \) de manera continua, por lo que son homotópicas.
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