AUTHORS: Rashmi Singh, Anuj Kumar Umrao

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Soft set theory is a useful mathematical tool to deal with uncertainty in a parametric manner. Near sets have been used as a tool to study extensions of topological spaces. The present paper introduces and studies nearness of finite order, 𝑆𝑆𝑛𝑛 − merotopy, in soft set theory. An 𝑆𝑆𝑚𝑚 − merotopic space (𝑈𝑈, 𝜁𝜁𝑚𝑚 ,𝐸𝐸) is introduced for a given 𝑆𝑆𝑛𝑛 − merotopic space (𝑈𝑈, 𝜁𝜁, 𝐸𝐸), where 𝑚𝑚 and 𝑛𝑛 are integers with the restriction that 2 ≤ 𝑚𝑚 ≤ 𝑛𝑛. For 𝑚𝑚 ≤ 𝑛𝑛 an 𝑆𝑆𝑛𝑛 − merotopy 𝜁𝜁∗ from a given 𝑆𝑆𝑛𝑛 − merotopy 𝜁𝜁 having the property that 𝜁𝜁 = (𝜁𝜁∗)𝑚𝑚 is constructed and the largest 𝑆𝑆𝑛𝑛 − merotopy having such property is derived. For an 𝑆𝑆𝑛𝑛 − merotopic space (𝑈𝑈, 𝜁𝜁), every maximal 𝜁𝜁 − compatible family is a maximal 𝜁𝜁 − clan.

KEYWORDS: Soft set; Grill operator; Soft Čech closure operator; Proximity spaces; Merotopic spaces

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