I'm attempting to construct a tikzpicture that looks like this:
Here's what I have:
\documentclass[12pt]{article}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage[english]{babel}
\usepackage[utf8x]{inputenc}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}
\usepackage{tkz-euclide}
\begin{document}
\begin{tikzpicture}[xscale=.6, yscale=.6]
\draw [<->,thick] (0,8) node [left] {$\mathbb{R}^{n}$}
|- (8,0);
\draw [<->,thick] (10,8) node [left] {$\mathbb{R}^{m}$}
|- (18,0);
\tkzDefPoint(4,1){A}
\tkzDefPoint(.5,3){B}
\tkzDefPoint(1,5){C}
\tkzDefPoint(1.2,7){D}
\tkzDefPoint(5.3,7.5){E}
\tkzDefPoint(7,6){F}
\tkzDefPoint(6,4){G}
\tkzDefPoint(6.7,3){H}
\draw [decoration={random steps,segment length=.75cm,amplitude=.5cm},
decorate, rounded corners=.3cm]
(A) -- (B) -- (C) -- (D) -- (E) -- (F) -- (G) -- (H) -- (A);
\draw [fill] (4,6) circle (.05) node [below] {$\bar{u}$};
\draw [dashed] (4,6) circle (1) node [below] {$B_{\delta}\left(\bar{u}\right)$};
\tkzDefPoint(14,1){I}
\tkzDefPoint(10.5,3){J}
\tkzDefPoint(11,5){K}
\tkzDefPoint(11.2,7){L}
\tkzDefPoint(15.3,7.5){M}
\tkzDefPoint(17,6){N}
\tkzDefPoint(16,4){O}
\tkzDefPoint(16.7,3){P}
\draw [decoration={random steps,segment length=.75cm,amplitude=.5cm},
decorate, rounded corners=.3cm]
(I) -- (J) -- (K) -- (L) -- (M) -- (N) -- (O) -- (P) -- (I);
\draw [fill] (14,3) circle (.05) node [above] {$f\left(\bar{u}\right)$};
\draw [dashed] (14,3) circle (1) node [below] {$f\left(B_{\epsilon}\left(\bar{u}\right)\right)$};
\end{tikzpicture}
\end{document}
Which produces:
And then my ineptitude became too frustrating.
Why do the blobs have tiny lines coming out of them every so often? Why are the corners of the blob at (4,1) and (14,1) not rounded? How do I correctly label the points and open balls? How do I create a tastefully bent arrow (as in the lines labeled "f")?
EDIT 1
Attempting to find the correct balance between segment length, amplitude, and rounded corner radii was cumbersome so I've settled for non-random blobs.
I took JLDiaz's suggestion in defining a tikzstyle but I don't think I fully understand what they meant. Here's what I have:
\documentclass[12pt]{article}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage[english]{babel}
\usepackage[utf8x]{inputenc}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[xscale=1, yscale=1]
\tikzstyle{ball}=[circle, dashed, minimum size=1cm, draw]
\tikzstyle{point}=[circle, fill, minimum size=.01cm, draw]
\draw [<->,thick] (0,8) node [left] {$\mathbb{R}^{n}$}
|- (8,0);
\draw [rounded corners=10pt] (4,1) -- (.5,3) -- (1,5) -- (1.2,7) -- (5.3,7.5) -- (7,6) -- (6,4) -- (6.7,3) --cycle;
\draw (4,6) node[point] (Point1) {};
\node [below] at (Point1) {$\bar{u}$};
\draw (4, 6) node[ball] (OpenBall1) {};
\node [below] at (OpenBall1) {$B_{\delta}\left(\bar{u}\right)$};
\end{tikzpicture}
\end{document}
Which produces:
The way I've set up the styles and nodes must be wrong because the desired effect has not taken place as JLDiaz described. What's the correct way to define these styles and nodes? Is there a way for tikz to see collisions and report an error on the console?
