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PreprintarXiv licencearXiv

The answer about Itzkowitz's Problems on FSIN groups

  • Dekui Peng
  • Li-Hong Xie
  • Jiang Yang
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Abstract

A topological group is functionally balanced if every bounded real-valued left uniformly continuous function is right uniformly continuous. We prove that every Hausdorff functionally balanced group has coinciding left and right uniformities, giving an affirmative answer to the Itzkowitz problem. Consequently, the classes of SIN, SFSIN and FSIN groups coincide.

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Cite

BibTeXRIS
BibTeX
@misc{peng2026answer,
  title = {{The answer about Itzkowitz's Problems on FSIN groups}},
  author = {Dekui Peng and Li-Hong Xie and Jiang Yang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07438},
  eprint = {2609.07438},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07438},
}
RIS
TY  - UNPB
TI  - The answer about Itzkowitz's Problems on FSIN groups
AU  - Dekui Peng
AU  - Li-Hong Xie
AU  - Jiang Yang
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.07438
UR  - https://arxiv.org/abs/2609.07438
AB  - A topological group is functionally balanced if every bounded real-valued left uniformly continuous function is right uniformly continuous. We prove that every Hausdorff functionally balanced group has coinciding left and right uniformities, giving an affirmative answer to the Itzkowitz problem. Consequently, the classes of SIN, SFSIN and FSIN groups coincide.
ER  -