New results regarding the lattice of uniform topologies on C(X)

• Pichardo-Mendoza, Roberto ^[1] ; Ríos-Herrejón, Alejandro ^[1]
  1. [1] Universidad Nacional Autónoma de México

     Universidad Nacional Autónoma de México

     México

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 24, Nº. 1, 2023, págs. 169-185
• Idioma: inglés
• DOI: 10.4995/agt.2023.18738
• Enlaces
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• Resumen

  • For a Tychonoff space X, the lattice UX  was introduced in L. A. Pérez-Morales, G. Delgadillo-Piñón, and R. Pichardo-Mendoza, The lattice of uniform topologies on C(X), Questions and Answers in General Topology  39 (2021), 65-71.

    In the present paper we continue the study of UX. To be specific, the present paper deals, in its first half, with structural and categorical properties of UX, while in its second part focuses on cardinal characteristics of the lattice and how these relate to some cardinal functions of the space X.

• Referencias bibliográficas
  • R. Engelking, General Topology, Sigma Series in Pure Mathematics, vol. 6, Heldermann Verlag, Berlin, 1989.
  • A. Hajnal and I. Juhász, Discrete subspaces of topological spaces, II, Indag. Math. 71, no. 1 (1970), 18-30. https://doi.org/10.1016/1385-7258(69)90022-5
  • R. Hodel, Cardinal Functions I, in: Handbook of Set-Theoretic Topology, K. Kunen and J. E. Vaughan, eds., Amsterdam (1984), 1-61. https://doi.org/10.1016/B978-0-444-86580-9.50004-5
  • R. Hodel, The number of closed subsets of a topological space, Canadian Journal of Mathematics 30, no. 2 (1978), 301-314. https://doi.org/10.4153/CJM-1978-027-7
  • T. Jech, Set Theory. The third millenium edition, revised and expanded, Springer Monograph in Mathematics, Springer-Verlag Berlin Heidelberg,...
  • S. Koppelberg, General Theory of Boolean Algebras, in: Handbook of Boolean algebras, J. D. Monk and R. Bonnet, eds., North-Holland, Amsterdam,...
  • K. Kunen, Set theory. An Introduction to Independence Proofs, Studies in Logic and the Foundations of Mathematics, vol. 102, North-Holland...
  • R. E. Larson and J. A. Susan, The lattice of topologies: A survey, The Rocky Mountain Journal of Mathematics 5, no. 2 (1975), 177-198. https://doi.org/10.1216/RMJ-1975-5-2-177
  • L. A. Pérez-Morales, G. Delgadillo-Piñón and R. Pichardo-Mendoza, The lattice of uniform topologies on C(X), Questions and Answers in General...
  • R. Pichardo-Mendoza, Á. Tamariz-Mascarúa and H. Villegas-Rodríguez, Pseudouniform topologies on C(X) given by ideals, Comment. Math. Univ....