What does the phrase "touch space" mean?

There's a mishearing somewhere along the line. The expression is touch base.

The expression means to have [brief] contact with someone (to exchange news & views, or simply to remind each other that you still exist and have some kind of relationship). It derives from baseball, where the hitter has to actually touch each base as he runs round. The important thing there is that there must be contact with the base.

Baseball also gives us the expression touch all bases (more commonly, cover all bases), meaning to have a plan which covers all foreseeable eventualities. That metaphoric usage alludes to the fact that every base that's being passed must be touched.

Here's a brief summary of both usages