Necessity of non-stratified and anti-stratified spaces in lattice-valued topology
This paper surveys the necessity of non-stratified spaces from these viewpoints: the characteristic functor, the L-spectrum and L-soberification functors, the upper free functor associated with L-valued frames, and two functorial embeddings associated with topological systems from semantic domains. Interestingly, additional arguments also emerge en mule for stratified spaces, so that this paper ultimately argues for the necessity of both stratified and non-stratified spaces in fixed-basis topology (the schemum of L-Top's) and variable-basis topology (e.g., Loc-Top). (C) 2009 Elsevier B.V. All rights reserved.
l-spectrum topological system fixed-basis topology variable-basis topology non-stratified/anti-stratified/normalized/conormalized/binormalized/hype rnormalized l-topological space l-top loc-top l-sobriety l-frame l-locale l-frm l-loc satisfaction relation topsys