subsets spatially far from each other) in X, as shown in Fig. 5. Let C^c = X \backslash C (complement of the set C). Then from the EF-axiom, observe the following: .
\begin{align} A\ &\underline{\delta}\ B,\\ B &\subset C,\\ D &= C^c,\\ X &= D \cup C,\\ A &\subset D,\ \mbox{hence, we can write}\\ A\ \underline{\delta}\ B\ &\Rightarrow\ A\ \underline{\delta}\ C\ \mbox{and}\ B\ \underline{\delta}\ D,\ \mbox{for some}\ C,D\ \mbox{in}\ X \mbox{ so that } C\cup D = X.