On the parallel between normality and extremal disconnectedness
-
Autores: Francisco Javier Gutierrez García
, Jorge Picado
- Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 218, Nº 5, 2014, págs. 784-803
- Idioma: inglés
- DOI: 10.1016/j.jpaa.2013.10.002
- Enlaces
-
Resumen
Severalfamiliarresultsaboutnormalandextremallydisconnected(classicalorpointfree)spacesshapetheideathatthetwonotionsaresomehowdualtoeachotherandcanthereforebestudiedinparallel.Thispaperinvestigatesthesourceofthis�duality�andshowsthateachpairofparallelresultscanbeframedbythe�same�proof.Thekeytoolsforthispurposearerelativenotionsofnormality,extremaldisconnectedness,semicontinuityandcontinuity(withrespecttoafixedclassofcomplementedsublocalesofthegivenlocale)thatbringandextendtolocaletheoryavarietyofwell-knownclassicalvariantsofnormalityandupperandlowersemicontinuitiesinanilluminatingunifiedmanner.Thisapproachallowsustounifyunderasinglelocalicproofallclassicalinsertion,aswellastheircorrespondingextensionresults.
¿Es nuevo? Regístrese
Ventajas de registrarse
