In this paper, the C̆ech fuzzy soft closure spaces are defined and their basic properties are studied. Closed (respectively, open) fuzzy soft sets is defined in C̆ech fuzzy-soft closure spaces. It has been shown that for each C̆ech fuzzy soft closure space there is an associated fuzzy soft topological space. In addition, the concepts of a subspace and a sum are defined in C̆ech fuzzy soft closure space. Finally, fuzzy soft continuous (respectively, open and closed) mapping between C̆ech fuzzy soft closure spaces are introduced. Mathematics Subject Classification: 54A40, 54B05, 54C05.

Highlights • In this work, some properties of Cech fuzzy soft closure spaces are introduced and studied. • Also, several types of lower separation axioms in Cech fuzzy soft closure space are introduced. • In addition, the relationship between these types of separation axioms are discussed. • Moreover, several examples are given to support our study.

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        The purpose of this work is to find maximum (k, n)-arcs from maximum (k, 2)-arcs where n=3,4,5.in the projective plane PG (2,5).