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

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

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Pichardo-Mendoza, R.; Ríos-Herrejón, A. (2023). New results regarding the lattice of uniform topologies on C(X). Applied General Topology. 24(1):169-185. https://doi.org/10.4995/agt.2023.18738

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/193027

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Título: New results regarding the lattice of uniform topologies on C(X)
Autor: Pichardo-Mendoza, Roberto Ríos-Herrejón, Alejandro
Fecha difusión:
Resumen:
[EN] 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 ...[+]
Palabras clave: Lattice of uniform topologies , Tychonoff spaces , Order-isomorphisms , Cardinal characteristics
Derechos de uso: Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
Fuente:
Applied General Topology. (issn: 1576-9402 ) (eissn: 1989-4147 )
DOI: 10.4995/agt.2023.18738
Editorial:
Universitat Politècnica de València
Versión del editor: https://doi.org/10.4995/agt.2023.18738
Código del Proyecto:
info:eu-repo/grantAgreement/CONACyT// 814282
Agradecimientos:
The research of the second author was supported by CONACyT grant no. 814282.
Tipo: Artículo

References

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. 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, 2003.

S. Koppelberg, General Theory of Boolean Algebras, in: Handbook of Boolean algebras, J. D. Monk and R. Bonnet, eds., North-Holland, Amsterdam, 1989.

K. Kunen, Set theory. An Introduction to Independence Proofs, Studies in Logic and the Foundations of Mathematics, vol. 102, North-Holland Publishing Co., Amsterdam, 1980.

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 Topology 39 (2021), 65-71.

R. Pichardo-Mendoza, Á. Tamariz-Mascarúa and H. Villegas-Rodríguez, Pseudouniform topologies on C(X) given by ideals, Comment. Math. Univ. Carolin. 54, no. 4 (2013), 557-577.

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