Derivative for Functions <i>f</i>:<i>G</i>→<i>H</i>, Where <i>G</i> Is a Metric Divisible Group

Abstract

In this paper, a derivative for functions f:G→H, where G is any metric divisible group and H is a metric Abelian group with a group metric, is defined. Basic differentiation theorems are stated and demonstrated. In particular, we obtain the Chain Role.

Keywords

• topological group
• homomorphism
• differentiability
• metric group
• locally compact space
• topological vector space