Hi all experts,(adsbygoogle = window.adsbygoogle || []).push({});

I've just visitted another Maths forum and picked up two interesting questions:

Question 1. Let H and K be homomorphic normed linear spaces. Is it necessary that H and K have the same dimension if both H and K are finite-dimension ? Is there possible a homomorphism between an infinite-dimension normed space and a finite-dimension one ?

Question 2. If f is a homomorphism between two normed linear spaces, is f necessary uniformly continuous ?

Hope to get your ideas.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homomorphic normed linear spaces

**Physics Forums | Science Articles, Homework Help, Discussion**