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In infinite dimensions, is it possible that convergence of distances to a sequence always implies convergence of that sequence?

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Prove $\int_{0}^{\infty} \cos(\omega x) \exp(-x^{\alpha}) \, {\rm d} x \ge {\alpha^2 \sqrt{\pi} \over 8} \exp \left( -\frac{\omega^2}{4} \right)$

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In infinite dimensions, is it possible that convergence of distances to a sequence always implies convergence of that sequence?

Étale cohmology is invariant under normalization?

Reference to a Classical Regularity Theorem

Relating smooth concordance and homology cobordism via integral surgeries

Prove compactness of approximate (finite differences) solutions of heat equation

Set theories without “junk” theorems?

Pushout of schemes and étale cohomology

Differential equation

Are there first-order statements that second order PA proves that first order PA does not?

Katz's proof of Cartier's (descent) theorem

Convolution of Standard Cauchy and Uniform points in the standard simplex

Diophantine equation of a factorial type

Prove $\int_{0}^{\infty} \cos(\omega x) \exp(-x^{\alpha}) \, {\rm d} x \ge {\alpha^2 \sqrt{\pi} \over 8} \exp \left( -\frac{\omega^2}{4} \right)$

A stronger Cauchy-Schwarz in infinite dimensional Hilbert spaces?

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