Is there a way to graphically imagine smash product of two topological spaces? Recently I've been reading "Topology" by Klaus Janich. I find this book very entertaining as it contains lots of graphical illustrations that appeal to my "geometrical" imagination. In paragraph 3.6 Janich gives nice illustrations of concepts such as "cone over a set" or "suspension". In the same paragraph he defines a smash product of two topological spaces. Yet, in the version of a book that I posses, there is no image that would present this concept. My question is therefore as in the title:

Is there a way to graphically imagine smash product of two topological spaces?

I'm not sure whether this question is suitable for MO. Perhaps I should put it into a comunity-wiki mode?
 A: To eloborate on what Arnav Tripathy said in a comment: if $X$ and $Y$ are compact, then $X \wedge Y$ is the one-point compactification of $(X \setminus \{x_0\}) \times (Y \setminus \{y_0\})$.
A: Here's a picture of a smash product that I drew for this talk, as far as I can tell it's what "Qfwfq" is describing in the middle paragraph.

A: As far as I remember, the smash product $X\wedge Y$ of two (pointed) spaces $(X,x_0)$ and $(Y,y_0)$ is obtained by taking the product of the two spaces $X\times Y$ and collapsing both the vertical "line" $\{x_0\}\times Y$ and the horizontal "line" $X\times\{y_0\}$ to a point.
So, if you (very loosely) imagine $X$ and $Y$ as segments, you can imagine $X\wedge Y$ as a square handkerchief which is shrinked along the central vertical and horizontal line, and the result is four "overhangs" coming out from the base point. [Of course the 4 overhangs are just an "artefact" of your simplified mental picture of the spaces $X$ and $Y$ as segments, it's not something general!]
Was I "graphical" enough?  :)
