@article{Abuzaid2024, 
author = {Dina Abuzaid and Samer Al Ghour},
title = {Three new soft separation axioms in soft topological spaces},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {2},
pages = {4632-4648},
keywords = {soft almost regularity, soft ω -openness, soft Rω-openness, soft regularity, soft ω -regularity, soft semi-regularity},
url = {https://www.sciopen.com/article/10.3934/math.2024223},
doi = {10.3934/math.2024223},
abstract = {Soft    ω-almost-regularity, soft    ω -semi-regularity, and soft    ω-       T          2              1        2             as three novel soft separation axioms are introduced. It is demonstrated that soft    ω -almost-regularity is strictly between "soft regularity" and "soft almost-regularity"; soft    ω-       T          2              1        2             is strictly between "soft        T          2              1        2            " and "soft        T          2      ", and soft    ω -semi-regularity is a weaker form of both "soft semi-regularity" and "soft    ω-regularity". Several sufficient conditions for the equivalence between these new three notions and some of their relevant ones are given. Many characterizations of soft    ω-almost-regularity are obtained, and a decomposition theorem of soft regularity by means of "soft    ω -semi-regularity" and "soft    ω-almost-regularity" is obtained. Furthermore, it is shown that soft    ω-almost-regularity is heritable for specific kinds of soft subspaces. It is also proved that the soft product of two soft    ω-almost regular soft topological spaces is soft    ω-almost regular. In addition, the connections between our three new conceptions and their topological counterpart topological spaces are discussed.}
}