Comment by aleph_minus_one

> Isn't there a less-conceptual (but still conceptual) problem that correctness of software is commonly abrupt rather than continuous? You don't get a series of almost-right programs gradually approximating the right program, you have a correct program and variations on it may fail completely.

I consider it to be plausible that such a topology could exist (at least for many situations). The problem rather is that such a topology would likely behave very different from users' expectations.