The algebraic face of the Alexandro one point compatication
Résumé
We give a characterization, in algebraic terms, of the Alexandroff one point compactication of a locally compact Hausdorff space. In fact, we prove that if (X, T) is a locally compact Hausdorff space, then (X', T') point compactication if and only if T is a maximal ideal of T'.
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Références
Barrıa, S. and Vielma, J., Topologies as Semirings: Prime Spectrum and an Application of the Stone Duality Theorem, Master Thesis, Universidad de Concepcion, Chile (2016).
Dedekind, R., Uber die Theorie der Ganzen Algebraiscen Zahlen , Supplement XI to P.G. Lejeune Dirichlet: Vorlesung Uber Zahlentheorie, Aufl., Druck und Verlag, Braunschweig 4, (1894).
Golan, J., Semirings and their Applications, Kluwer Academic Publisher, (2010).
Guale, A. and Vielma, J., The algebraic face of the Collatz conjecture, Preprint (2019).
Munkres, J., Topologıa, Prentice Hall, New Jersey, United States (2002).
Vandiver, H., Note on a simple type of algebra in which cancellation law of addition does not hold, Bull. Amer. Math. Soc. 40, 914-920, (1934). https://doi.org/10.1090/S0002-9904-1934-06003-8
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Funding data
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Escuela Superior Politécnica del Litoral
Grant numbers FCNM-09-2017
