TY - JOUR
AU - Rodabaugh, S.E.
PY - 2008/04/01
Y2 - 2024/06/20
TI - Functorial comparisons of bitopology with topology and the case for redundancy of bitopology in lattice-valued mathematics
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 9
IS - 1
SE -
DO - 10.4995/agt.2008.1871
UR - https://ojs.upv.es/index.php/AGT/article/view/1871
SP - 77-108
AB - <p>This paper studies various functors between (lattice-valued) topology and (lattice-valued) bitopology, including the expected “doubling” functor E<sub>d</sub> : L-Top â†’ L-BiTop and the “cross” functor E× : L-BiTop â†’ L<sup>2</sup>-Top introduced in this paper, both of which are extremely well-behaved strict, concrete, full embeddings. Given the greater simplicity of lattice-valued topology vis-a-vis lattice-valued bitopology and the fact that the class of L2-Top’s is strictly smaller than the class of L-Top’s encompassing fixed-basis topology, the class of E×’s makes the case that lattice-valued bitopology is categorically redundant. As a special application, traditional bitopology as represented by BiTop is (isomorphic in an extremely well-behaved way to) a strict subcategory of 4-Top, where 4 is the four element Boolean algebra; this makes the case that traditional bitopology is a special case of a much simpler fixed-basis topology.</p>
ER -