# All Questions

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### Point Set Topology Puzzle

Choose A, a subset of some topological space X. If we are given the closure and complement operations, how many distinct subsets of X can we create? How can we choose A to maximize this number? I ...
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### Relation between different definitions of degree in complex geometry

Consider a holomoprhic map from a Riemann surface $$f: \Sigma_g \to \mathbb{CP}^n.$$ This is given by some homogeneous polynomials in some variables. How can we show that the homogeneous degree $d$ ...
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### Alternative proof of 'a linegraph of a Hamiltonian graph is Hamiltonian'?

So I've got an assignment to proof that the linegraph of a normal Hamiltonian graph is also Hamiltonian (but not Eulerian most of the time). I've found that this is a direct corollary of a theorem of ...
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### Use of “for all” in definition of reflexive and symmetric relations.

My book says that a relation R on A is reflexive, if $\ (a,a) \in R, \ for\ every \ a \in A$ symmetric, if $\ (a_1,a_2) \in R \implies (a_2,a_1) \in R,\ for\ all\ a_1,a_2 \in A$ Although I ...
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### Spectral decomposition of normal operator

Define $T$ from $L_{2}(R)$ into itself by $T(f)(t)=f(t+1)$. Show that $T$ is normal and finds its spectral decomposition. I've shown that $f$ is normal (in fact it's unitary) but how do I find its ...
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### Find the next divisor without remainder

I divide a value and if the remainder is not 0 I want the closest possible divisor without remainder. Example: I have: $100 \% 48 = 4$ Now I am looking for the next value which divide 100 wihtout ...
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### Find the polynomials wich are solution for a diferential equation

Find all the polynomials grade $\leqslant 2$ wich are solution for: $x^{2}y^{'}+(x+1)y=x^{3}$ I'm lost here, i don't understand what is asking for exactly. So mi attempt to do it is find the ...
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### Correct equation

What is the correct equation which describes the following dates: 270, 180, 135, 112.25, 101.25. I've obtained data whit the equations: 180 + 90 = 270 135 + 45 = 180 112.5 + 22.5 = ...
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### Help with this proof (Index Sifting)

Let $(x_j)^\infty_{j=1}$ be a sequence in $\mathbb{Z}$ and let $a, b, r \in \mathbb{Z}$ such that $a\le b$. Then $\sum\limits_{j=a}^b x_j = \sum\limits_{j=a+r}^{b+r} x_{j-r}$ I assume that I would ...
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### Ordinal Arithmetic sufficient condition that a + c < b + c

I know that in general ordinal addition is not strictly increasing in the left argument (as in $0+ \omega = n+\omega$). Now I have a fixed countable ordinal $\delta$ and a natural number $k$. My ...