When is a space Menger at infinity?

Menger probabilistic normed space is a category topological vector space

In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...

menger probabilistic normed space is a category topological vector space

in this paper, we formalize the menger probabilistic normed space as a category in which its objects are the menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. so, we can easily apply the results of topological vector spaces...

Regularity at space-like and null infinity

We extend Penrose’s peeling model for the asymptotic behaviour of solutions to the scalar wave equation at null infinity on asymptotically flat backgrounds, which is well understood for flat space-time, to Schwarzschild and the asymptotically simple space-times of Corvino-Schoen/Chrusciel-Delay. We combine conformal techniques and vector field methods: a naive adaptation of the “Morawetz vector...

Blow-up at space infinity for nonlinear heat equations

On Blow-up at Space Infinity for Semilinear Heat Equations

We are interested in solutions of semilinear heat equations which blow up at space infinity. In [7], we considered a nonnegative blowing up solution of ut = ∆u+ u, x ∈ R, t > 0 with initial data u0 satisfying 0 ≤ u0(x) ≤ M, u0 ≡ M and lim |x|→∞0 = M, where p > 1 and M > 0 is a constant. We proved in [7] that the solution u blows up exactly at the blow-up time for the spatially constant solution...