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seen Nov 15 at 1:57

An amateur general topology researcher.


Nov
14
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
Nov
14
accepted The term “maximal solution” for PDE
Nov
14
asked The term “maximal solution” for PDE
Nov
14
answered Solution of a differential equation having a singularity (not everywhere defined)
Nov
14
comment Solution of a differential equation having a singularity (not everywhere defined)
See my above comment about general relativity
Nov
14
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
Nov
14
comment Solution of a differential equation having a singularity (not everywhere defined)
Your answer does not rule out $\mathbb{R}\setminus\mathbb{N}$ for $y^\prime =y^2$
Nov
13
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 $C_2$
Nov
13
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
Nov
13
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?
Nov
13
revised Solution of a differential equation having a singularity (not everywhere defined)
edited tags
Nov
13
asked Solution of a differential equation having a singularity (not everywhere defined)
Nov
12
comment An implication involving filters
It seems there is an error in your proof: "$x_I\in I$, and $x_J\in J$" should be instead "$x_I\in I$, or $x_J\in J$"
Nov
12
comment An implication involving filters
Oh, I have understood
Nov
12
comment An implication involving filters
What is $(K\in x)$?
Nov
11
comment An implication involving filters
@dfeuer: I've added more parentheses
Nov
11
revised An implication involving filters
added 6 characters in body
Nov
11
comment An implication involving filters
@BrianM.Scott: I've corrected my question
Nov
11
revised An implication involving filters
added 97 characters in body
Nov
11
asked An implication involving filters