On inductive and inverse limits of systems of compact metric spaces and applications

TL;DR

This paper establishes the existence of inductive and inverse limits in categories of compact metric spaces and groups, providing foundational results and applications in the field.

Contribution

It proves the existence of inductive and inverse limits in categories of compact metric spaces and groups, expanding the theoretical framework.

Findings

Existence of inductive limits in compact metric spaces and groups.

Existence of inverse limits in these categories.

Applications demonstrating the utility of these limits.

Abstract

The aim of this paper is to prove the existence of inductive and inverse limits of direct and inverse systems in a certain category of compact metric spaces as well as of compact metric groups. Some applications are presented.