# Simple way to prove compactness of closed intervals in simply ordered set with order topology

## TL;DR

This paper introduces a simplified proof demonstrating the compactness of closed intervals within simply ordered sets equipped with the order topology.

## Contribution

It provides a more straightforward method for establishing the compactness of closed intervals in these ordered topological spaces.

## Key findings

- Simplified proof of compactness for closed intervals
- Enhanced understanding of order topology properties
- Potential for easier teaching and application of these concepts

## Abstract

In this note, we present a simpler way to prove the compactness of the closed intervals in simply ordered set with order topology.