# Topology-bornology as a basis of turbulence

1. Aug 12, 2013

### greentea28a

According to Wikipedia bornology is the minimum amount of structure needed to address boundedness. Topology is the minimum amount of structure needed to address continuity.

Topology-bornology (cf. Bornologies and Fuctional Analysis, by Hogbe-Nlend) can be applied to Distributions as bounded linear functionals, Differential Operators, PDEs, Differential Polynomials; Laplacian and Heat operator.

However, bornologies by itself is not so useful so we look at his second book Nuclear and Conuclear Spaces. We want to extend topology-bornology the space to nuclear space because it is "nicer". These spaces inherit properties of Schwartz space. Referring to Wikipedia again, elements of vector spaces in nuclear spaces are smooth.

I've learned about bornologies, Schwartz spaces, and nuclear spaces from the aforementioned books. Did I stumble upon the mathematics of turbulence?

Last edited: Aug 12, 2013