Tagged Questions

219 views

Finding a good ordering of $\mathbb{Q}$

Oftentimes in density arguments we let $\{x_n\}$ be a dense sequence and this is sufficient to imply the desired result. From a research question I am working on I have simplified the ...
156 views

Topological conditions forcing continuity

Let $X$, $Y$, and $Z$ be topological spaces. Let $f:X \rightarrow Y$. Further assume that for every continuous function $g:Y \rightarrow Z$, $g \circ f$ is continuous. Question: Under what ...
541 views

A question about measurable structures on function spaces

Hey, I was just wondering, I'm using some of Robert Aumann's ideas about measurable structures on function spaces (From his paper 'Borel structures for Function spaces': ...
224 views

For METRIZABLE spaces, do the Banach classes and Baire classes coincide?

In this paper: 'Borel structures for Function spaces' by Robert Aumann, http://projecteuclid.org/euclid.ijm/1255631584 Aumann claims that when X and Y are metric spaces (among other things), the ...
327 views

Does anyone know an example of non-separable $L^1$ of a probability space?

It is easy to give examples of non-separable $L^p$ spaces by considering a measure on a big space. If one adds the condition that the space has to have total measure 1, the problem is not as easy. ...
413 views

Extending Continuous Sublinear maps on dense subsets of a Banach space

Suppose X' and Y are Banach spaces and X is a linear subspace dense in X'. Let T be a continuous map of X to Y satisfying: (1) ||T(x+y)|| is less than or equal to ||T(x)||+||T(y)||. Please prove ...
368 views

Is there a non-trivial example for a 1-homogeneous function satisfying a specific inequality of second order?

Hello everybody, Actually, I'm thinking about the following problem: Let $\mathbb{R}^n$ be the $n$-dimensional real vector space with Cartesian coordinates $x=(x^1,\ldots, x^n)\in \mathbb{R}^n$. I'm ...
Given a constant $k \in \mathbb N$, and a set of $p$ multi-variate polynomials {$P_j:\mathbb N^n\to \mathbb Z$}$\_{j=1...p}$, with $P_j \not\equiv 0$. Is the following true: There exists $n$ sets ...
Consider the tiling of the Poincare disk $\mathbb{D}$ by identified octagons (i.e., representing a torus with genus 2). Suppose inside each octagon is a subset A such that the octagon minus A is a ...