On soft compact and soft Lindelöf spaces via soft regular closed sets

Soft ω-regular open sets and soft nearly Lindelöfness

“…So, we have 𝑧 ∈ 𝐺(𝑒) ⊆ 𝑈. Also, by Proposition 3.28 of [54], 𝐺(𝑒) ∈ 𝑅𝑂(𝑍, 𝜌 𝑒 ). Hence, (𝑍, 𝜌 𝑒 ) is semi regular.…”

“…Since (𝑍, 𝜌 𝑒 ) is semi regular, then there exists 𝑉 ∈ 𝑅𝑂(𝑍, 𝜌 𝑒 ) such that 𝑧 ∈ 𝑉 ⊆ 𝐹(𝑒). Thus, we have 𝑒 𝑧 ∈𝑒 𝑉 ⊆𝐹 and by Proposition 3.28 of [54], 𝑒 𝑉 ∈ 𝑅𝑂(𝑍, ⊕ 𝑒∈𝐸 𝜌 𝑒 , 𝐸). It follows that (𝑍, ⊕ 𝑒∈𝐸 𝜌 𝑒 , 𝐸) is soft semi regular.…”

“…So, there exists 𝑈 ∈ 𝑅𝑂(𝑍, 𝜌 𝑒 ) such that 𝑧 ∈ 𝑈 and 𝑈 − 𝐺(𝑒) is countable. Now, we have 𝑒 𝑧 ∈𝑒 𝑈 and by Proposition 3.28 of [54], 𝑒 𝑈 ∈ 𝑅𝑂(𝑍, ⊕ 𝑒∈𝐸 𝜌 𝑒 , 𝐸). Moreover, 𝑒 𝑈 − 𝐺 ∈ 𝐶𝑆𝑆(𝑍, 𝐸).…”

“…So, there exists 𝑅 ∈ 𝑅𝑂(𝑍, ⊕ 𝑒∈𝐸 𝜌 𝑒 , 𝐸) such that 𝑒 𝑧 ∈𝑅 and 𝑅 − 𝐺 ∈ 𝐶𝑆𝑆(𝑍, 𝐸). By Proposition 3.28 of [54], 𝑅(𝑒) ∈ 𝑅𝑂(𝑍, 𝜌 𝑒 ). Moreover, since 𝑅 − 𝐺 ∈ 𝐶𝑆𝑆(𝑍, 𝐸), then 𝑅(𝑒) − 𝐺(𝑒) = (𝑅 − 𝐺) (𝑒) is countable.…”

L-esnek topolojik uzaylar arasındaki dönüşümler için sürekliliğin derecelendirmesi

“…Inspring by this idea, mathematicians working in the pure sciences embedded these set theories to their own branches. Up to now, lots of spectacular and creative researches about the theories of soft sets and the fuzzy soft sets have been considered by some scholars (Roy & Maji, 2007;Çetkin, 2019;Terepeta, 2019;Kocinac et al, 2021;Al-jarrah et al, 2022;Çetkin, 2022).…”