答案1
我认为你确实应该自己尝试一下。
\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{fit,shapes.geometric}
\begin{document}
\begin{tikzpicture}[bullet/.style={circle,fill,inner sep=2pt}]
\draw[very thick,blue,fill=blue!10] (-6,-3) rectangle (6,3)
node[below right]{$X$};
\draw[very thick,green!70!black,fill=green!10] (-4.8,-1) rectangle (4.8,2.8)
node[below right]{$Y$};
\draw[very thick,red,fill=red,fill opacity=0.1] (0,0) circle[radius=2cm];
\draw[very thick] (-120:2) node[bullet,label=below:$x_0$] (x0){}
-- ++ (120:3.5) node[midway,below left]{$\|x_0-y\|>1-\varepsilon$}
node[bullet,purple,label=above:$y$](y){};
\draw[thick,orange] (x0) -- (x0|-0,-1) node[midway,right]{$1-\varepsilon$};
\end{tikzpicture}
%
\begin{tikzpicture}[bullet/.style={circle,fill,inner sep=2pt}]
\draw (0,0) node[bullet,label=below:$x$] (M){}
node[circle,draw,very thick,blue,dashed,minimum
size=2cm,label={right:$B(x,r)$}] (C) {};
\draw[thick,yellow!80!black] (M) -- ++ (110:2) node[near end,left] {$d$} coordinate (aux);
\draw[very thick,cyan] (aux) ++(200:2)coordinate(aux2)
-- ++(20:4) node[pos=1.05] (Y){$Y$};
\draw[red,very thick] (M) -- (20:1) node[midway,above]{$r$};
\node[draw,red!80!black,very thick,ellipse,fit=(C)(Y)(aux2),minimum width=10cm,
label={[red!80!black]20:$X$}]{};
\end{tikzpicture}
%
\begin{tikzpicture}[bullet/.style={circle,fill,inner sep=2pt}]
\draw (0,0) node[bullet,label=below:$x$] (M){}
node[circle,draw,very thick,blue,dashed,minimum
size=2cm,label={right:$B(x,r)$}] (C) {};
\draw[thick,yellow!80!black] (M) -- ++ (110:2) node[near end,left] {$d$} coordinate (aux);
\draw[very thick,cyan] (aux) ++(200:2)coordinate(aux2)
-- ++(20:4) node[pos=0.6,bullet,green!50!yellow,label=above:$y^*$]{}
coordinate[pos=0.7] (P) node[pos=1.05] (Y){$Y$};
\draw[red,very thick] (M) -- (20:1) node[midway,above]{$r$};
\node[draw,red!80!black,very thick,ellipse,fit=(C)(Y)(aux2),minimum width=10cm,
label={[red!80!black]20:$X$}]{};
\draw[thick,orange] (M) -- (P) node[right,near end]{$d/(1-\varepsilon)$};
\end{tikzpicture}
\end{document}
