3 papers
math.CT2021
On the Cantor and Hilbert Cube Frames and the Alexandroff-Hausdorff Theorem
Francisco Ávila, Julio Urenda, Angel Zaldívar
The aim of this work is to give a pointfree description of the Cantor set. It can be shown that the Cantor set is homeomorphic to the -adic integers $\mathbb{Z}_{p}:=\{x\in\math…
math.GN2019
The Frame of Nuclei of an Alexandroff Space
Francisco Ávila, Guram Bezhanishvili, Patrick Morandi +1
Let be the frame of open sets of a topological space , and let be the frame of nuclei of . For an Alexandroff space , we prove…
math.GN2019
When is the frame of nuclei spatial: A new approach
Francisco Ávila, Guram Bezhanishvili, Patrick Morandi +1
For a frame , let be the Esakia space of . We identify a special subset of consisting of nuclear points of , and prove the following results: is sp…