Alright, thx for the answer although I am not sure why would you choose that exact comment to make on a dead account. Why not anything else? Anyhow...thx for remembering me about my old account here.
o.O haven't checked this website in years. I even forgot I had an account here and I just got an email notification due to your comment. I'm curious what made you comment this? I genuinely don't remember.
Tychonoff Plank is a topological space which is defined as the product of the set of all ordinals which are less than or equal to ω (the first infinite ordinal) and the set of all ordinals which are less than or equal to ω1 (first uncountable ordinal) with the product topology that is induced on it.
The tychonoff plank is normal but its subset, the punctured tychonoff plank (tychonoff plank-(ω,ω1)) is not. It is an example that shows that normal spaces can have subsets that are not normal.
The Mittag-Leffler theorem says that any meromorphic function F(z) with given poles An can be expanded in the neighbourhood of one of its poles in terms of some entire function (function that's holomorphic on the finite complex plane) H(z) and the principal part (negative power part in the Laurent series) of that function for that pole.
F(z)=H(z)+∑(from n=1 to ∞)[Gn(z)+Pn(z)]
here Gn(z) is the principal part corresponding to the pole An and Pn(z) is chosen based on Gn(z) so that the series is uniformly convergent.
The Cross Product (also known as vector product) of two vectors belonging to R3 is the vector that is orthogonal to the original vectors (orientation is given by right hand rule) and whose length is equal to the area of the parallelogram formed by the two vectors.
(I know there are other cross products but this was the easiest one :)
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The tychonoff plank is normal but its subset, the punctured tychonoff plank (tychonoff plank-(ω,ω1)) is not. It is an example that shows that normal spaces can have subsets that are not normal.
Green's Function
Normal Space
F(z)=H(z)+∑(from n=1 to ∞)[Gn(z)+Pn(z)]
here Gn(z) is the principal part corresponding to the pole An and Pn(z) is chosen based on Gn(z) so that the series is uniformly convergent.
Uniform Convergence
(I know there are other cross products but this was the easiest one :)
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