Whitney Properties and Whitney reversible properties of Cut and Non-Cut Points

@misc{matsuhashi2026whitney,
  title = {{Whitney Properties and Whitney reversible properties of Cut and Non-Cut Points}},
  author = {Eiichi Matsuhashi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.31034},
  eprint = {2609.31034},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31034},
}

TY  - UNPB
TI  - Whitney Properties and Whitney reversible properties of Cut and Non-Cut Points
AU  - Eiichi Matsuhashi
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.31034
UR  - https://arxiv.org/abs/2609.31034
AB  - In this paper, we study several properties concerning cut points and non-cut points. First, we show that the property of being a continuum consisting entirely of shore points is preserved under refinable maps. Next, we show that having a block point, having a non-shore point, and having a strong center point are not Whitney-reversible properties. Consequently, \cite[Question 2.9]{nonweak} has a negative answer. Furthermore, we show that none of the classes of continua witnessing the failure of the sequential strong Whitney-reversible property for these three properties admits a common model. Finally, in connection with the fact that colocal connectedness is not a Whitney-reversible property, we show that the class of nonaposyndetic continua having a cut point and such that every positive Whitney level is colocally connected has no common model.
ER  -