ν-compact relative to X

Definition

• A subset S of a space X is ν-compact relative to X if for each ν-open cover {V_α : α ∈ ∇} of S by ν-open sets of X for each α∈∇, ∃ F_α∈RC(X) \ni F_α⊂V_α and S⊂∪{(F_α)^o:α∈∇} there exists a finite subset ∇_0 of ∇ such that S ⊂ ∪{F_α:α∈∇_0}

Property

• If A is ν-compact subspace of a topological space X, then A is ν-compact relative to X.

Reference

• S. Balasubramanian, C.Sandhya and P.Aruna Swathi Vyjayanthi, Note on Regularity and ν-compactness, Int. J. Contemp. Math. Sciences, Vol. 5, (2010) no. 16, 777-784