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تسجيل مستخدم جديدTwo extensions of the Stone Duality to the category of zero-dimensional Hausdorff spaces
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Extending the Stone Duality Theorem, we prove two duality theorems for the category ZHaus of zero-dimensional Hausdorff spaces and continuous maps. Both of them imply easily the Tarski Duality Theorem, as well as 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.
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In [G. Dimov and E. Ivanova-Dimova, Two extensions of the Stone Duality to the category of zero-dimensional Hausdorff spaces, arXiv:1901.04537v4, 1--33], extending the Stone Duality Theorem, we proved two duality theorems for the category ZDHaus of z
ero-dimensional Hausdorff spaces and continuous maps. Now we derive from them the extension of the Stone Duality Theorem to the category BooleSp of zero-dimensional locally compact Hausdorff spaces and continuous maps obtained in [G. Dimov, Some generalizations of the Stone Duality Theorem, Publicationes Mathematicae Debrecen, 80 (2012), 255--293], as well as two new duality theorems for the category BooleSp.
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