Homomorphic images of algebraic groups

TL;DR

This paper investigates the conditions under which algebraic groups over local fields maintain closed images when mapped continuously into arbitrary topological groups, enhancing understanding of their topological group properties.

Contribution

It provides new criteria for the closedness of images of algebraic groups over local fields under continuous homomorphisms, advancing the theory of their topological behavior.

Findings

Identifies conditions ensuring closed images of algebraic groups over local fields.

Establishes criteria for continuous homomorphisms preserving closedness.

Enhances understanding of topological properties of algebraic groups.

Abstract

We study topological group theoretic properties of algebraic groups over local fields. In particular, we find conditions under which such groups have closed images under arbitrary continuous homomorphisms into arbitrary topological groups.