An application of the Stone-Weierstrass Theorem

• García-Máynez, Adalberto ^[1] ; Gary, Margarita ^[2] ; Pimienta, Adolfo ^[3]
  1. [1] Universidad Nacional Autónoma de México

     Universidad Nacional Autónoma de México

     México

     
  2. [2] Universidad del Atlántico

     Universidad del Atlántico

     México

     
  3. [3] Universidad Simón Bolívar.

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• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 42, Nº. 5, 2023, págs. 1211-1220
• Idioma: inglés
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• Resumen

  • Let (X, τ) be a topological space, we will denote by |X|,|X|K, |X|τ and |X|δ, the cardinalities of X; the family of compacts in X; the family of closed in X, and the family of Gδ-closed in X, respectively. The purpose of this work is to establish relationships between these four numbers and conditions under which two of them coincide or one of them is ≤ c, where c denotes, as usual, the cardinality of the set of real numbers R. We will use the Stone-Weierstrass theorem to prove that: Let (X, τ) be a compact Hausdorff topological space, then |X|δ ≤ |X|ℵ0