Two problems of SI-compact spaces

Zhengmao He

Two problems of SI-compact spaces

General Topology 2026-08-03 v1

Authors: Zhengmao He

Abstract

Zhao and Ho use the irreducible open cover family respected with the Scott topology to introduce the SI-compactness. It has been proved that the SI-compactness is strictly stronger than compactness. In this paper, we prove that the product of finitely many SI-compact spaces is always SI-compact which gives a positive answer for the question posed by Zhao and Ho. Furthermore, we show that the category of all SI-compact spaces is not a reflective full subcategory of TOP.

Cite

@article{arxiv.2608.02020,
  title  = {Two problems of SI-compact spaces},
  author = {Zhengmao He},
  journal= {arXiv preprint arXiv:2608.02020},
  year   = {2026}
}