Volume 26 , Issue 3 , PP: 202-220, 2025 | Cite this article as | XML | Html | PDF | Full Length Article
Samer Al-Ghour 1 * , Dina Abuzaid 2
Doi: https://doi.org/10.54216/IJNS.260314
This work adds to the burgeoning knowledge of soft topology. First, we continue the study of soft locally closed sets. We present several characterizations of soft locally closed sets. Also, we investigate their behaviors using specialized soft topologies as product and subspace soft topologies. Then, we define and investigate the concept of soft dense-in-itself spaces. In particular, we characterize soft dense-in-itself subspaces in terms of locally closed sets. Given a soft topological space pN, ρ, Mq, the collection of soft locally closed sets of pN, ρ, Mq forms a soft topology on N relative to M which is denoted by ρl. We obtain several symmetries between the pN, ρ, Mq and pN, ρl, Mq. In particular, we show that pN, ρ, Mq is soft T0 (resp. soft TD, soft indiscrete) iff pN, ρl, Mq is soft T0 (resp. soft discrete, soft connected). Moreover, we show that if pN, ρl, Mq is soft T1 (resp. soft Alexandroff), then pN, ρl, Mq is soft discrete (resp. soft Alexandroff) but not conversely. In addition to these, we obtain several characterizations and relationships of both soft locally indiscrete spaces and soft submaximal spaces. In particular, we show that pN, ρ, Mq is soft locally indiscrete if and only if ρ “ ρl. In the last section, via the soft locally closed sets, we define and investigate soft lc-regularity as a stronger form of soft regularity. Finally, the paper deals with the correspondence between some concepts in soft topology and their analog concepts in classical topology.
Soft locally closed sets , Soft submaximal spaces , Soft Alexandroff spaces , Soft locally indiscrete spaces , Soft regular spaces
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