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Pointfree Functorial Polar Functions


C denotes the category of compact regular frames with frame homomorphisms. A function \(\mathcal {X}\), which assigns to each C-object F a subalgebra of \(\mathcal {P}(F)\) that contains the complemented elements of F is said to be a polar function. An essential extension H of F is a \(\mathcal {X}\)-splitting frame of F if whenever \(p \in \mathcal {X}(F)\), then the polar generated by p in H is complemented. For F∈ C we examine the least \(\mathcal {X}\)-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.

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Correspondence to Ricardo E. Carrera.

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Carrera, R.E. Pointfree Functorial Polar Functions. Appl Categor Struct 24, 37–52 (2016).

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  • Pointfree polar functions
  • Functorial polar functions
  • Hull class
  • Skeletal maps
  • Compact regular frame
  • α-disconnected frame
  • α-cloz frame

Mathematics Subject Classification (2010)

  • 06D22
  • 18A99