Minimal R_1, minimal regular and minimal presober topologies

TL;DR

This paper characterizes minimal R_1 and minimal regular topologies using filters within specific intervals of non-trivial R_0 topologies, advancing the understanding of their structural properties.

Contribution

It introduces filter-based characterizations of minimal R_1 and minimal regular topologies in certain topological intervals.

Findings

Filter-based characterizations of minimal R_1 topologies

Filter-based characterizations of minimal regular topologies

Insights into the structure of non-trivial R_0 topologies

Abstract

By means of filters, minimal R_1 and minimal regular topologies are characterized on suitable intervals consisting of non-trivial R_0 topologies.