Continuous lattices of quotient objects in the category of compacta

Authors

  • O.R. Nykyforchyn Vasyl Stefanyk Carpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine; Casimir the Great University in Bydgoszcz, 30 J.K. Chodkiewicza str., 85064, Bydgoszcz, Poland
  • K.M. Koporkh Vasyl Stefanyk Carpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
  • O.Ya. Mykytsey Vasyl Stefanyk Carpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
https://doi.org/10.15330/cmp.18.2.409-419

Keywords:

"way below" relation, "way above" relation, approximation relation, quotient object, compactum
Published online: 2026-08-07

Abstract

We describe approximation relations "way below" and "way above" on the poset of quotient objects of a compact Hausdorff space. Necessary and sufficient conditions are established for a quotient object to be the exact bound of quotient objects approximating it. It is shown that such objects form algebraic or dually algebraic lattices.

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How to Cite
(1)
Nykyforchyn, O.; Koporkh, K.; Mykytsey, O. Continuous Lattices of Quotient Objects in the Category of Compacta. Carpathian Math. Publ. 2026, 18, 409-419.