locally ν-compact

Definition

• Topological space X is said to be locally ν-compact space if every x in X has a ν-neighborhood? whose closure is ν-compact.

Property

• Every ν-compact space is locally ν-compact.
• If f : (X,τ) → (Y,σ) is ν-irresolute?, ν-open and X is locally ν-compact,then so is Y.
• ν-closed subset of a locally ν-Compact space is locally ν-Compact.
• countable product of locally ν-Compact spaces is locally ν-Compact.
• countable union of locally ν-Compact spaces is locally ν-Compact.

Reference

• S. Balasubramanian, P. Aruna Swathi Vyjayanthi and C. Sandhya,ν-Compact spaces , Scientia Magna, international book series, Vol. 5 (2009), No. 1 (78-82)