# Colombeau algebras without asymptotics

## TL;DR

This paper introduces a new construction of Colombeau-type algebras of generalized functions that relies solely on topological estimates rather than asymptotic estimates, simplifying the framework.

## Contribution

It provides a novel approach to defining Colombeau algebras using topological estimates instead of asymptotic regularization parameters.

## Key findings

- Constructed Colombeau algebras using topological estimates.
- Avoided asymptotic estimates in the algebra definition.
- Simplified the theoretical framework for generalized functions.

## Abstract

We present a construction of algebras of generalized functions of Colombeau-type which, instead of asymptotic estimates with respect to a regularization parameter, employs only topological estimates on certain spaces of kernels for its definition.