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 Nov16 accepted A function continuous in both arguments Nov16 accepted “Uniform groups” (similar to topological groups)? Nov16 accepted Double embedding or double restriction Nov16 accepted Check a theorem about the category Set Nov16 accepted Solution of a differential equation having a singularity (not everywhere defined) Nov16 accepted A proposition about filters on cartesian product of two sets Nov16 accepted An implication involving filters Nov15 revised Is a set closed under finite intersections? (about filters) added 1 characters in body Nov15 asked Is a set closed under finite intersections? (about filters) Nov14 comment The term “maximal solution” for PDE But how the "physical" solutions of general relativity can be defined? If we don't require maximality of the solution domain, then our world would be seriously damaged by having a solution only 1cm in size instead of the full universe Nov14 accepted The term “maximal solution” for PDE Nov14 asked The term “maximal solution” for PDE Nov14 answered Solution of a differential equation having a singularity (not everywhere defined) Nov14 comment Solution of a differential equation having a singularity (not everywhere defined) See my above comment about general relativity Nov14 comment Solution of a differential equation having a singularity (not everywhere defined) There should be an answer. For example, in GR the solution is defined on the entire space except of black holes. It isn't an arbitrarily chosen part of space Nov14 comment Solution of a differential equation having a singularity (not everywhere defined) Your answer does not rule out $\mathbb{R}\setminus\mathbb{N}$ for $y^\prime =y^2$ Nov13 comment Solution of a differential equation having a singularity (not everywhere defined) What I remember exactly from my study in a university is that for a DE like this there was solution like $f(t)+C_1$ for $t<1$ and $f(t)+C_2$ for $t>1$. In the definition I search for the solution was not on an interval but on the union of two intervals with different independent constants $C_1$ and $C_2$ Nov13 comment Solution of a differential equation having a singularity (not everywhere defined) As far as I remember when I studied the empty function was not a solution. In your definition nothing prevents to consider empty function as a solution. I want a more exact definition Nov13 comment Solution of a differential equation having a singularity (not everywhere defined) Thanks for the example, but I also want an exact definition which makes this into a solution. (I don't see the reason why it is allowed to be undefined in one particular point.) Why empty function (the function having empty set as the domain) is not also a solution? Nov13 revised Solution of a differential equation having a singularity (not everywhere defined) edited tags