Generalized topology and the family of monotonic maps $$\Gamma (X)$$ Γ ( X )

Abstract

Abstract 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.

Keywords

• Family of monotonic maps $$\Gamma (X)$$ Γ ( X )
• Cs $$\acute{a}$$ a ´ zs $$\acute{a}$$ a ´ r generalized topological space
• Interesting monotonic maps $$\{int_{\delta }, cl_{\delta }, \sigma , \alpha , \pi , \beta \}$$ { i n t δ , c l δ , σ , α , π , β }