Open AccessTwo extensions of the stone duality to the category of zero-dimensional Hausdorff spaces
Author(s) -
Georgi Dimov,
Elza Ivanova-Dimova
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2106851d
Subject(s) - mathematics , hausdorff space , duality (order theory) , zero (linguistics) , urysohn and completely hausdorff spaces , tychonoff space , corollary , pure mathematics , paracompact space , normal space , arzelà–ascoli theorem , hausdorff measure , topological vector space , topological space , hausdorff dimension , fixed point theorem , brouwer fixed point theorem , danskin's theorem , philosophy , linguistics
Extending the Stone Duality Theorem, we prove two duality theorems for the category ZHaus of zero-dimensional Hausdorff spaces and continuous maps. They extend also the Tarski Duality Theorem; the latter is even derived from one of them. We prove as well two new duality theorems for the category EDTych of extremally disconnected Tychonoff spaces and continuous maps. Also, we describe two categories which are dually equivalent to the category ZComp of zero-dimensional Hausdorff compactifications of zero-dimensional Hausdorff spaces and obtain as a corollary the Dwinger Theorem about zero-dimensional compactifications of a zero-dimensional Hausdorff space.