Some results on weaker forms of starn-CCC, weakly Lindelöf and starn-DCCC spaces
Submitted: 2023-05-30
|Accepted: 2024-05-01
|Published: 2024-10-01
Copyright (c) 2024 Ricardo Cruz-Castillo, Alejandro Ramírez-Páramo, Jesús F. Tenorio
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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Keywords:
Cardinality, covering, rank l-diagonal, star-P spaces, weakly (almost) star-CCC spaces, weakly (almost) star-DCCC spaces, weakly (almost) star-weakly Lindelöf spaces
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Abstract:
In this paper we provide some general results about topological spaces X which satisfy starn- P , weakly starn- P and almost starn- P, for P∈ { κ ᴄᴄ , W κ L , ᴅ κ ᴄᴄ } , where κ is an infinite cardinal number.
The particular cases when κ = ω , P ∈ { ᴄᴄᴄ , weakly Lindelöf , ᴅ ᴄᴄᴄ } are obtained. Furthermore, for the same classes of spaces defined by such P, by applying Erdős-Radó's theorem and using the rank l-diagonal notion, we establish some cardinal inequalities.
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