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Article
Pointfree Functorial Polar Functions
Applied Categorical Structures
  • Ricardo Enrique Carrera, Nova Southeastern University
Document Type
Article
Publication Date
2-1-2016
Keywords
  • Pointfree polar functions,
  • Functorial polar functions,
  • Hull class,
  • Skeletal maps,
  • Compact regular frame,
  • α-disconnected frame,
  • α-cloz frame
Disciplines
Peer Reviewed
1
Abstract
C denotes the category of compact regular frames with frame homomorphisms. A function XX , which assigns to each C-object F a subalgebra of P(F)P(F) that contains the complemented elements of F is said to be a polar function. An essential extension H of F is a XX -splitting frame of F if whenever p∈X(F)p∈X(F) , then the polar generated by p in H is complemented. For F∈ C we examine the least XX -splitting extension and prove that every invariant polar function generates a C-hull class of frames. In addition, we define the concept of a functorial polar function and prove that each functorial polar function generates an epireflective subcategory of the category compact regular frames with skeletal maps.
DOI
10.1007/s10485-014-9385-4
Citation Information
Ricardo Enrique Carrera. "Pointfree Functorial Polar Functions" Applied Categorical Structures Vol. 24 Iss. 1 (2016) p. 37 - 52 ISSN: 0927-2852
Available at: http://works.bepress.com/ricardo-carrera/16/