Topologically seperated

trambolin

Hi there,

I am kind of blocked by the "topologically seperated" phrase in the following sense. The reading comes to the paragpraph as such

"... Relations are topologically seperated, loosely speaking, if the distance from points of one relation to the other grows without bound....."

Anyone can shed some light on this? Especially if we have two graphs :

[tex]
\begin{array}{l}
G_1 = \left\{ {\left( {\begin{array}{*{20}c}
x \\
y \\
\end{array}} \right):x = Ay} \right\} \\
G_2^- = \left\{ {\left( {\begin{array}{*{20}c}
x \\
y \\
\end{array}} \right):y = Bx} \right\} \\
\end{array}
[/tex]

It is said that "bla bla bla ... if and only if the graph of A and the inverse graph of B are topologically seperated i.e. [itex]G_1 \cap G_2^- = \{0\}[/itex]" Let's keep A,B linear for now. I don't get how come the two sentences are related in a topological sense.

Thanks