This is both a math and biology question but I think it makes more sense for a biologist to answer it. My question is: what can be said, if anything, about the space of all possible human DNAs (for a suitable definition of "human" in the context of this question)? Is it open or closed with respect to a suitable topology?
EDIT: To fix ideas and make it less a matter of opinion, one (admittedly incomplete, this is for the sake of making the question more precise) definition to use might be "those who can reproduce with existing fertile human beings"?
EDIT 2: To be clear, I am not a biologist but a computer scientist and maybe my question is guided by assumptions that simply do not hold. My naive vision of someone's DNA is a string of A,T,G,C which, when "interpreted", becomes that person. I am also under the impression that a single mutation of a letter may render them nonviable. On the other hand, other mutations may produce an individual with altered characteristics, who may or may not be able to reproduce with other human beings. So I was wondering if there is an interesting way to think of the space (in a mathematical sense) of all strings of DNA which produce a viable human being in this sense. If my assumption that a single mutation can render one nonviable, I would expect that this space would be "closed" for some topology. I'm totally ready to accept that this way of thinking about DNA is flawed and/or unrealistic, and in that case I'd be happy to learn why, if possible in layman's terms.