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. Of course, whether this is literally true depends on what sort of algorithmic problem you're approaching. But there must be man…
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.