A space X is said to be cellular-Lindelöf if for every cellular family U there is a Lindelöf subspace L of X which meets every element of U. Cellular-Lindelöf spaces generalize both Lindelöf spaces and spaces with the countable chain condition. Solving questions of Xuan and Song, we prove that every cellular-Lindelöf monotonically normal space is Lindelöf and that every cellular-Lindelöf space with a regular Gδ -diagonal has cardinality at most 2c. We also prove that every normal cellular-Lindelöf first-countable space has cardinality at most continuum under 2
A. Bella, S. Spadaro (2019). Cardinal invariants of cellular Lindelof spaces. REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS, FÍSICAS Y NATURALES. SERIE A, MATEMÁTICAS, 113(3), 2805-2811 [10.1007/s13398-019-00660-1].
Cardinal invariants of cellular Lindelof spaces
S. Spadaro
2019-01-01
Abstract
A space X is said to be cellular-Lindelöf if for every cellular family U there is a Lindelöf subspace L of X which meets every element of U. Cellular-Lindelöf spaces generalize both Lindelöf spaces and spaces with the countable chain condition. Solving questions of Xuan and Song, we prove that every cellular-Lindelöf monotonically normal space is Lindelöf and that every cellular-Lindelöf space with a regular Gδ -diagonal has cardinality at most 2c. We also prove that every normal cellular-Lindelöf first-countable space has cardinality at most continuum under 2File | Dimensione | Formato | |
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