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Let $X=S^2$ be the unit sphere in $mathbb{R}^3$ and $T:Xrightarrow mathbb{R}$ be a continuous function. My topology textbook claims that the set $A={x in X |...
1Mathematics Asked by Roberto Faedda on 2 years ago
I am following a proof of the following statements: if $f:Xto Y$ is a morphism of varieties (say, quasi-projective), then the graph of $f$, i.e. the subset ...
1Mathematics Asked by Redundant Aunt on 2 years ago
After encountering many numerical problems related to finding real roots of a polynomial, I have fixed a simple path:For an odd-degree polynomial: complex roots come in pairs. If a...
1Mathematics Asked on 2 years ago
Consider the following double integral: $$ int int_{S} (x+z) dS$$ Over the region in first octant of plane $ x+y+z=1$ I know the bounds are : $$...
2Mathematics Asked on 2 years ago
We define a set $X$ as compact if: "for every open cover of $X$, there exists a finite subcover." An Open Cover $C$ of $X$ is...
1Mathematics Asked on 2 years ago
$Q)$ There are fields $mathbb{Q} subset F subset K$ (Here the $mathbb{Q}subset $F and $mathbb{Q}subset $ K are Galois extension) Say the $f(x) in ...
1Mathematics Asked on 2 years ago
Let $f(x, y)$ be a real valued function defined on the real domain $X times Y$ which is integrable in the Riemann or Lebesgue sense (or any other...
0Mathematics Asked by Tom Collinge on 2 years ago
Suppose I take a space $M$ of smooth functions $rho:Xrightarrowmathbb{R}$, and I give $M$ some manifold structure (perhaps as a Banach or Hilbert manifold?). Then if I...
0Mathematics Asked on 2 years ago
Let $A$ and $B$ be two non empty finite sets. Also, $A cap B = varnothing$. Then I have to prove that $A cup B $...
0Mathematics Asked on 2 years ago
An easy corollary of the Szemerédi Regularity Lemma is that dense graphs contain linear sized $varepsilon$-regular bipartite subgraphs whose density is similar to that of the parent graph. As...
1Mathematics Asked by alpmu on 2 years ago
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