From A-spaces to arbitrary spaces via spatial fibrous preorders

TL;DR

This paper introduces spatial fibrous preorders, extending the known equivalence between preorders and Alexandrov spaces to a broader class of topological spaces, thereby generalizing the foundational relationship in topology.

Contribution

It proposes the concept of spatial fibrous preorders and establishes their equivalence with arbitrary topological spaces, expanding the theoretical framework.

Findings

Introduces spatial fibrous preorders as a new notion.

Extends the preorder-space equivalence to all topological spaces.

Provides a foundational generalization in topology.

Abstract

The well known equivalence between preorders and Alexandrov spaces is extended to an equivalence between arbitrary topological spaces and spatial fibrous preorders, a new notion to be introduced.