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PreprintCC BY 4.0arXiv

Two problems of SI-compact spaces

  • Zhengmao He
Open at sourcePDFDOICite

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 arbitrary product of 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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Cite

BibTeXRIS
BibTeX
@misc{he2026problems,
  title = {{Two problems of SI-compact spaces}},
  author = {Zhengmao He},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.02020},
  eprint = {2608.02020},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.02020},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Two problems of SI-compact spaces
AU  - Zhengmao He
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2608.02020
UR  - https://arxiv.org/abs/2608.02020
AB  - 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 arbitrary product of 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.
ER  -