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

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