Two problems of SI-compact spaces

Zhengmao He

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arXiv · 2608.02020

Two problems of SI-compact spaces

Zhengmao He

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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.

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Zhengmao He. 2026-08-03. Two problems of SI-compact spaces. https://arxiv.org/abs/2608.02020

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