# All Questions

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### $f$ analytic such that $f (z)$ has only essential singularity

Let $f$ be analytic such that $1/f(z)$ has only essential singularity. Then which of the following hold? a) $f$ must be a polynomial. b) $f$ cannot be a polynomial. c) $f (1/z)$ must have a pole. ...
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### nonlinear pde equation

I want to solve the problem: find some non-trivial particular solution of nonlinear PDE. Are the any methods for this? I understand that there is no general method to find general solution, but.. One ...
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### If $(M_{\lambda})$ be a chain of closed affine subspaces of $X$ $\Longrightarrow$ $\displaystyle \bigcap_{\lambda\in L} M_{\lambda}\neq \emptyset \;$?

Let $X$ be a Banach space Let $(M_{\lambda})_{\lambda \in L}$ be a chain of closed affine subspaces of $X$ We can say that $$\displaystyle \bigcap_{\lambda\in L} M_{\lambda}\neq \emptyset \;\;?$$ ...
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### Doubt with bounds and integrand of $\int_{0}^{2\pi}\int_{0}^{\pi/2}\int_{0}^{2}\rho^2\sin{\phi}d\rho d\phi d\theta$

Question as follows. Find the volume of the solid enclosed between the spheres $x^2+y^2+z^2=4$ and $x^2+y^2+z^2=4z \Leftrightarrow x^2+y^2+(z-2)^2=4$. I constructed the following integral and after ...
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### Show $X=\left\{x \in [0,1]: x \neq \frac1n\text{ for any }n \in \Bbb N\right\}$ is neither compact nor connected
I am stuck on the following question: Let $X=\{x \in [0,1]: x \neq \frac1n: n \in \Bbb N\}$ be given the subspace topology. Then I have to prove that $X$ is neither compact nor connected. Can ...