The categorical relationships between neighborhood spaces, T-neighborhood spaces and stratified L-neighborhood spaces

Abstract

In this paper, for a complete residuated lattice L, we present the categorical properties of T-neighborhood spaces and their categorical relationships to neighborhood spaces and stratified L-neighborhood spaces. The main results are: (1) the category of T-neighborhood spaces is a topological category; (2) neighborhood spaces can embed in T-neighborhood spaces as a reflective subcategory, and when L is a meet-continuous complete residuated lattice, L-neighborhood spaces can embed in stratified L-neighborhood spaces as a reflective subcategory; (3) when L is a continuous complete residuated lattice, neighborhood spaces (resp., T-neighborhood spaces) can embed in T-neighborhood spaces (resp., stratified L-neighborhood spaces) as a  simultaneously reflective and coreflective subcategory.