ON PROPERTIES OF GENERALIZED NEIGHBOURHOOD SYSTEMS

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Güner E., Sağıroğlu Peker S.

Universitatis Scientiarum Budapestinensis de Rolando Eotvos nominatae, vol.57, pp.33-42, 2014 (Peer-Reviewed Journal)

• Publication Type: Article / Article
• Volume: 57
• Publication Date: 2014
• Journal Name: Universitatis Scientiarum Budapestinensis de Rolando Eotvos nominatae
• Page Numbers: pp.33-42
• Ankara University Affiliated: Yes

Abstract

Neighbourhood structures are particular cases of generalized neighbourhood systems. Let X=∅ be a set and N(X) be the set of all neighbourhood structures on X, partially ordered as follows:ψ≤φ for ψ,φ∈N(X) iff ψ(x)≤φ(x) for each x∈X. Then N(X) is a complete sublattice of the GN(X) which denotes the set of all  strongly  generalized neighbourhood systems on X partially ordered as above.We investigate some properties  of GN(X). In addition we discuss the product of generalized  neighbourhood systems and present some new results concerning gn-continuity related tot his product.