# All Questions

0answers
95 views

### Does there exist a continuous surjection? [on hold]

Let $C$ be an irreducible projective cubic in $\mathbb{P}_2$ with a singular point $p$. So consider $f: \mathbb{P}_1 \to C$ defined as follows. Identify $\mathbb{P}_1$ with the set of lines in ...
0answers
75 views

2answers
217 views

### Is Eilenberg-Maclane $\wedge$ Moore space the spectrum of the cohomology theory $H^*(\ ,G)$?

In the web page http://www.encyclopediaofmath.org/index.php/Moore_space it can be found the following statement: If $K(\mathbb Z,n)$ is the Eilenberg–MacLane space of the group of integers ...
2answers
593 views

### Polish by compact is Polish?

Let $X,Y$ be separable and metrizable, with $Y$ Polish, and suppose there is a topological quotient map $f:X\to Y$ with compact fibers. Is $X$ Polish? I have a specific space in mind, so if the ...
1answer
37 views

### Intersection of complements of connected components (2)

Let $(X,d)$ be a non-compact, complete metric space and $K\subseteq X$ compact. Pick $x^* \in X\setminus K$. Let $E$ be the connected component of $X\setminus K$ that contains $x^*$. Let ${\cal C}$ ...
2answers
100 views

### Isomorphism problem on the class of induced subgraphs of a hypercube

A problem that I am currently studying translates to the problem of deciding whether two induced subgraphs of the hypercube $Q_k$ are isomorphic. Now it feels to me that this class of graphs is "too ...
1answer
94 views

### application of factorization theorem

Young's inequlity tells us that $L^{1}(\mathbb R)\ast L^{p}(\mathbb R) \subset L^{p}(\mathbb R)$ with norm inequality $$\|f\ast g\|_{L^{p}} \leq \|f\|_{L^1}\|g\|_{L^p};$$ and of course this ...
0answers
26 views

0answers
21 views

### Compute eigenvalues and lash1e vectors (2n + 1) X (2n + 1) matrix: [on hold]

middle row: 1 ... 1 0 1 ... 1 middle column: 1 ... 1 0 1 ... 1 In the unmarked places are zero. Calculate at least in the case, when n=2 I have really no idea how to start.
0answers
10 views

### Cardinality of maximum independent set for a given degree distribution

Consider undirected graph $G(V,E)$. Assume that $f_n(k)$ be the probability mass function of degree of a vertex in $G$. Further, assume that $f_n(k)$ is an strictly decreasing function of $k$ with ...
2answers
137 views

### Closure of the graph of a function

Let $X_1, X_2$ be non-empty sets and let $R\subseteq X_1\times X_2$ such that for all $x\in X_1$ there is $y\in X_2$ such that $(x,y)\in R$. Are there topologies $\tau_i$ on $X_i$ for $i=1,2$ and a ...
0answers
29 views

### Cartopolar curve

Is there any plane curve that has the same equation in cartesian as in polar coordinates? To be more specific, is there a function such that $f(f(x)\cos x)=f(x)\sin x, \forall x$?
1answer
64 views

### planes intersecting a convex polytope

We are given a $d$-dimensional convex polytope ${\cal P}$ in $N$-dimensional space where $d<N-1$. Consider several planes $P_i$ corresponding to inequalities $f_i(X)\ge 0$. We are given that each ...
0answers
42 views

### What is the complexity of finding a generator for the cyclic elliptic curves?

Let $E$ be an elliptic curve which is defined over a finite field $\mathbb{F}_p$, where $p$ is a prime number. If we know that $E(\mathbb{F}_p)$ is cycyclic, is there an algorithm to find its ...
0answers
39 views

### Equivalence (or not) of two Artin/Fox wild arcs

The repeating patterns in the wikipedia articles on wild arcs and wild knots seem to me to be not continuously deformable to each other. Is this true? For clarity, here is my diagram of the repeating ...
0answers
116 views

### Varieties acted upon faithfully by an abelian variety

Let $X$ be a smooth projective variety over the complex numbers. Suppose that some positive-dimensional abelian variety $A$ acts faithfully on $X$. Examples of such varieties $X$ are provided by ...
1answer
177 views

### When a smooth algebra is regular?

Let $A \subseteq B$ be noetherian integral domains, $A$ regular (=every localization at maximal ideal is a regular local ring) and $B$ is a smooth $A$-algebra. For the definition of a smooth algebra, ...
2answers
667 views

### Origin of the term “Diophantine equation”

It seems that the term "Diophantine equation" has been around at least since the second half of the 19th century, since the historian Hermann Hankel writes (polemically) in the chapter on Diophantus ...
1answer
733 views

### When is there a submersion from a sphere into a sphere?

(First posted on math.SE, with no answers.) That is: For which positive integers $n, k \ge 1$ does there exist a submersion $S^{n+k} \to S^k$? The discussion at this math.SE question has ...
0answers
33 views

0answers
79 views

### Problem with operator and Fourier transform

I am currently dealing with a problem in functional analysis where I want to show the following. Let $\phi_{k+1}(x):=\sqrt{2} \sum_{n \in \mathbb{Z}} h(n) \phi_k(2x-n)$ and $\phi_0= \chi_{[0,1]},$ if ...
0answers
16 views

### Calculate coordinate transformation matrix [on hold]

Calculate coordinate transformation matrix A in the base [1; x; x2]. In the space R2 [x] of real polynomials highest rate? D is given a scalar product. Sebi-adjoint transformation of A: R2 [x]! R2 ...
2answers
171 views

### Convergence of a sum with the ranks of homotopy groups

Let $F$ be a (nontrivial) topological space that satisfies the following conditions: 1) $\pi_n(F)$ has a trivial action of $\pi_1(F)$ for $n>0$ and 2) its homology groups are finitely generated. ...
0answers
21 views

### Definite integral involving Legendre Polynomial [on hold]

Does anyone know the answer to the following definite integral: $\displaystyle \int_{0}^{\pi}P_{\ell}(\cos\theta)\sin^{k}\theta\, d\theta$, for $k\geq 1$, where $P_{\ell}(x)$ is the $\ell$-th ...
2answers
200 views

### Radial limit does not exist almost everywhere

Problem 4 in Chapter 4 of Stein's book "Real Analysis" says $\sum_{n\geqslant 0}z^{2^n}$ doesn't have radial limit as $z$ approaches the unit circle from inside almost everywhere. It's fairly easy ...

15 30 50 per page