All topologies come from a family of 0-1 valued quasimetrics

TL;DR

This paper proves that every topology can be derived from a family of 0-1 valued quasimetrics, establishing a fundamental connection between topology and a specific class of metrics.

Contribution

It introduces a novel characterization showing that all topologies are generated by 0-1 valued quasimetrics, unifying topology with a simple metric framework.

Findings

All topologies are obtainable from 0-1 valued quasimetrics.

The result bridges topology and metric spaces in a new way.

Provides a foundation for further exploration of quasimetrics in topology.

Abstract

We prove the statement in the title.