AI 中文总结
本文针对SI-紧空间的两个问题，证明有限个SI-紧空间的乘积仍为SI-紧空间，正面回应了前人的问题，并得出SI-紧空间范畴不是TOP的反射满子范畴的结论。
AI 中文摘要
赵和何利用Scott拓扑下的不可约开覆盖族引入了SI-紧性，已证明SI-紧性严格强于紧性。本文证明有限个SI-紧空间的乘积仍是SI-紧空间，正面回答了赵和何提出的问题；还证明所有SI-紧空间构成的范畴不是TOP的反射满子范畴。
英文摘要
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.
