Construction of topologies, filters and uniformities for a product of sets

TL;DR

This paper introduces a method to construct topologies, filters, and uniformities on product sets based on filters over index sets and the structures of coordinate sets.

Contribution

It develops a systematic approach to define these structures in product spaces using filters over index sets and coordinate set structures.

Findings

Provides a new framework for constructing topologies and uniformities on product spaces.

Extends the theory of filters to product set constructions.

Lays groundwork for further research in product space topologies.

Abstract

Starting from filters over the set of indices, we introduce structures in a product of sets where the coordinate sets have the given structures.