Soft Bitopological Spaces via Soft Elements
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915779677519872 |
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| author | Ray, S. |
| author_facet | Ray, S. |
| contents | We introduce soft bitopological spaces from the standpoint of soft elements. A soft bitopological space is a soft set equipped with two soft topologies. Following the classical construction of Goldar--Ray, each soft topology on $F$ induces an ordinary topology on the set $\SE(F)$ of soft elements; hence every soft bitopological space canonically determines a genuine bitopological space on $\SE(F)$. Within this setting we define pairwise soft separation axioms ($T_0$, $T_1$, $T_2$) and a notion of pairwise soft compactness, and we compare them with their parameterwise counterparts. For canonical (sectionwise generated) soft bitopologies, we show that the pairwise soft $T_i$ axioms are equivalent to the corresponding pairwise $T_i$ axioms on each parameter space. Compactness exhibits a finiteness phenomenon: when the parameter set is finite, componentwise pairwise compactness forces pairwise soft compactness, while an infinite-parameter example shows that the finiteness assumption is essential. Examples are included to clarify how the induced bitopology on $\SE(F)$ may behave differently from the original soft bitopology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06372 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Soft Bitopological Spaces via Soft Elements Ray, S. General Topology 54A05, 54D10, 03E72 We introduce soft bitopological spaces from the standpoint of soft elements. A soft bitopological space is a soft set equipped with two soft topologies. Following the classical construction of Goldar--Ray, each soft topology on $F$ induces an ordinary topology on the set $\SE(F)$ of soft elements; hence every soft bitopological space canonically determines a genuine bitopological space on $\SE(F)$. Within this setting we define pairwise soft separation axioms ($T_0$, $T_1$, $T_2$) and a notion of pairwise soft compactness, and we compare them with their parameterwise counterparts. For canonical (sectionwise generated) soft bitopologies, we show that the pairwise soft $T_i$ axioms are equivalent to the corresponding pairwise $T_i$ axioms on each parameter space. Compactness exhibits a finiteness phenomenon: when the parameter set is finite, componentwise pairwise compactness forces pairwise soft compactness, while an infinite-parameter example shows that the finiteness assumption is essential. Examples are included to clarify how the induced bitopology on $\SE(F)$ may behave differently from the original soft bitopology. |
| title | Soft Bitopological Spaces via Soft Elements |
| topic | General Topology 54A05, 54D10, 03E72 |
| url | https://arxiv.org/abs/2602.06372 |