are you talking about mathematical limits? perhaps if you explained more about what you meant by "limits ... in metric spaces". i mean, why only metric spaces and not spaces measured in feet, yards, or miles, or lightyears... however, if you're speaking in mathematical terms of, say, calculus, then, limits are infinite. there is no convergence, ever. the space may be amazingly small, but the space remains.
the full name of the theory is, "einstein's theory of general relativity". i don't remember anyone ever formally pronouncing it fact. it remains, in the scientific community, a theory. sure, it has been a useful theory, but a theory, it remains.
i don't know anything about nash because i did not watch "a beautiful mind". ron howard films suck, imho, and i do not have the money for college right now.
"theory" in webster's dictionary: 2.) proposed explanation whose status is still conjectural
5.) a particular conception or view of something to be done or of the method of doing it. (pertains to collection of data and examination of same).
7.) contemplation or speculation.
near as i can tell, people use the word "theory" to say, "until we have a better answer this will have to do".
say evolution over creationism.
evolution is an argument, whereas, creationism is a quarrel. no one means to say that evolution is an answer, rather that it is a way of arriving at answers. that is, until a better means is stumbled upon.
creationism is a quarrel, the idea pivots around a creator, is this supposed to be a new argument? next, you'll bust out with the supposedly fresh idea that the earth is the center of the universe, or that the earth is flat... suppose for a minute that you weren't looking for evidence of the creator in the data, but rather how the processes changed over time and that you could prove these things mathematically with the materials you had available to you...
the problem that arises is when people have all the information they need and arrive at completely wrong answers; like when good meaning people read the new testament, call themselves christian, and decide to kill planned parenthood clinicians. that type of thing. or did i misread the question?