  For a finite discrete topological space $X$ with at least two elements, a
nonempty set $\Gamma$, and a map $\varphi:\Gamma\to\Gamma$,
$\sigma_\varphi:X^\Gamma\to X^\Gamma$ with
$\sigma_\varphi((x_\alpha)_{\alpha\in\Gamma})=
(x_{\varphi(\alpha)})_{\alpha\in\Gamma}$ (for $(x_\alpha)_{\alpha\in\Gamma}\in
X^\Gamma$) is a generalized shift. In this text for
$\mathcal{S}=\{\sigma_\psi:\psi\in\Gamma^\Gamma\}$ and
$\mathcal{H}=\{\sigma_\psi: \Gamma\mathop{\rightarrow}\limits^{\psi}\Gamma$ is
bijective$\}$ we study proximal relations of transformation semigroups
$(\mathcal{S},X^\Gamma)$ and $(\mathcal{H},X^\Gamma)$. Regarding proximal
relation we prove: \[P({\mathcal
S},X^\Gamma)=\{((x_\alpha)_{\alpha\in\Gamma},(y_\alpha)_{\alpha\in\Gamma}) \in
X^\Gamma\times X^\Gamma: \exists\beta\in\Gamma\:(x_\beta=y_\beta)\}\] and
$P({\mathcal H},X^\Gamma)\subseteq
\{((x_\alpha)_{\alpha\in\Gamma},(y_\alpha)_{\alpha\in\Gamma}) \in
X^\Gamma\times X^\Gamma: \{\beta\in\Gamma:x_\beta=y_\beta\}$ is
infinite~$\}\cup\{ (x,x):x\in \mathcal{X}\}$. \\ Moreover, for infinite
$\Gamma$, both transformation semigroups $({\mathcal S},X^\Gamma)$ and
$({\mathcal H},X^\Gamma)$ are regionally proximal, i.e., $Q({\mathcal
S},X^\Gamma)=Q({\mathcal H},X^\Gamma)=X^\Gamma \times X^\Gamma$, also for
sydetically proximal relation we have $L({\mathcal
H},X^\Gamma)=\{((x_\alpha)_{\alpha\in\Gamma},(y_\alpha)_{\alpha\in\Gamma}) \in
X^\Gamma\times X^\Gamma: \{\gamma\in\Gamma:x_\gamma\neq y_\gamma\}$ is
finite$\}$.
