3D surface and topology I was reading an article that mentioned "a  connected surface in 3D space with $\infty$ many ends (in the topologocal sense)".
I have read the wiki page on "ends" but couldn't make much sense of it, not to mention being able to come up/ visualise such a surface! Help would be very much appreciated.
 A: Let $\pi_0 (Y)$ denote the set of connected components of a topological space $Y$. (This usually means the set of path-connected components of $Y$, but for our purposes here this is more convenient.) The set of ends of $X$ is the subset $E$ of the cartesian product $\prod_K \pi_0 (X \setminus K)$, where $K$ varies over all the compact subsets of $X$, defined by the following condition: $(U_\bullet) \in E$ just if for every pair of compact subsets $K$ and $K'$, there is a compact subset $K''$ such that $K'' \subseteq K \cap K'$ and $U_K \cup U_{K'} \subseteq U_{K''}$.
Intuitively, an end of $X$ is a connected component of $X$ ‘at infinity’. For example, you may wish to verify that $\mathbb{R}$ has two ends, $\mathbb{R}^2$ has one end, and $[0, 1]$ has no ends. As suggested in the comments, there are many intuitive objects which have infinitely many ends. A tree which bifurcates forever would be my favourite.
A: http://www.math.indiana.edu/gallery/minimalSurface.phtml 
has infinitely many ends
