No abstract

No abstract

The goal of this paper is to introduce and study the induced proximity on a fuzzy space due to the existence of a fuzzy proximity on another fuzzy space. Firstly, for every two complete lattices L, M, it is defined and studied the extension of the () * *

In this paper, interesting properties of the generalized topological spaces, generated by the monotonic maps $$\sigma = (cl_{\delta }\circ int_{\delta }),$$ σ = ( c l δ ∘ i n t δ ) , $$\alpha = (int_{\delta }\circ cl_{\delta }\circ int_{\delta }),$$ α = ( i n t δ ∘ c l δ ∘ i n t δ ) , $$\pi = (int_{\delta }\circ cl_{\delta })$$ π = ( i n t δ ∘ c l δ ) and $$\beta = (cl_{\delta }\circ int_{\delta }\circ cl_{\delta }),$$ β = ( c l δ ∘ i n t δ ∘ c l δ ) , for any generalized topological space $$(X,g_{\delta })$$ ( X , g δ ) are deduced and analyzed. Special subfamilies of the family of monotonic maps $$\Gamma (X)$$ Γ ( X ) are studied and interesting results regarding generalized topologies are obtained.