Geodesic
Dimension in soft topological space
Nečetkie sistemy i mâgkie vyčisleniâ, Tome 11 (2016) no. 1, pp. 5-18.

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The notion of dimension, based on family of coverings, is constructed for soft topological space. Some simplest properties of dimension are presented. Dimension of finite spaces and compact sets are investigated. Examples of calculation of the dimension are considered.
Keywords: soft topology, soft dimension of a set. 
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D. A. Molodtsov. Dimension in soft topological space. Nečetkie sistemy i mâgkie vyčisleniâ, Tome 11 (2016) no. 1, pp. 5-18. http://geodesic.mathdoc.fr/item/FSSC_2016_11_1_a0/

[1] Molodtsov D. A., “Soft topological structures”, Nechetkie Sistemy i Myagkie Vychisleniya [Fuzzy Systems and Soft Computing], 10:2 (2015), 115–153 (in Russian) | MR

[2] Aleksandrov P. S., Pasynkov B. A., Introduction to the Theory of Dimension, Nauka Publ., Moscow, 1973 (in Russian) | MR