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

Author:

Li Lingqiang1,Jin Qiu1,Bo Chunxin1,Xiu Zhenyu2

Affiliation:

1. Department of Mathematics, Liaocheng University, Liaocheng, P.R. China

2. College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, China

Abstract

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

Publisher

National Library of Serbia

Subject

General Mathematics

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