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The categorical relationships between neighborhood spaces, ┬-neighborhood spaces and stratified L-neighborhood spaces
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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.
Title: The categorical relationships between neighborhood spaces, ┬-neighborhood spaces and stratified L-neighborhood spaces
Description:
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.
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