Listar Artículo en revista de investigación por autor "0000-0002-1727-3895"
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On the Cantor and Hilbert cube frames and the Alexandroff-Hausdorff theorem
Ávila Álvarez, Francisco (2021-10-01)The aim of this work is to give a point-free description of the Cantor set. It can be shown that the Cantor set is homeomorphic to the p-adic integers for every prime number p. To give a point-free description of the Cantor ... -
The Frame of Nuclei on an Alexandroff Space
Ávila Álvarez, Francisco (2020-06-20)Let O𝑆 be the frame of open sets of a topological space S, and let 𝑁(O𝑆) be the frame of nuclei on O𝑆. For an Alexandroff space S, we prove that 𝑁(O𝑆) is spatial iff the infinite binary tree 𝒯2 does not embed ... -
The frame of the p-adic numbers and a p-adic Version of the Stone-Weierstrass Theorem in Pointfree Topology
Ávila Álvarez, Francisco (2020-03-15)The algebraic nature of a frame allows its definition by generators and relations. Joyal used this to introduce the frame of the real numbers and Banaschewski studied this frame with a particular emphasis on the pointfree ... -
When is the frame of nuclei spatial: A new approach
Ávila Álvarez, Francisco (2020-07-01)For a frame L, let XL be the Esakia space of L. We identify a special subset YL of XL consisting of nuclear points of XL, and prove the following results: • L is spatial iff YL is dense in XL. • If L is spatial, then ...