Some observations on compact indestructible spaces

TL;DR

This paper investigates properties of compact indestructible spaces, establishing their sequential compactness, finite derived set property in Lindelof Hausdorff cases, and pseudoradiality in compact Hausdorff cases, inspired by recent work.

Contribution

It provides new results linking indestructibility with classical compactness properties in topology, extending previous research.

Findings

Compact indestructible spaces are sequentially compact.

Lindelof Hausdorff indestructible spaces have the finite derived set property.

Compact Hausdorff indestructible spaces are pseudoradial.

Abstract

Inspired by a recent work of Dias and Tall, we show that a compact indestructible space is sequentially compact. We also prove that a Lindelof Hausdorff indestructible space has the finite derived set property and a compact Hausdorff indestructible space is pseudoradial.