We establish several bounds on the cardinality of a topological space involving the Hausdorff pseudocharacter H psi (X). This invariant has the property psi(c)(X) <= H psi( X) <= chi(X) for a Hausdorff space X. We show the cardinality of a Hausdorff space X is bounded by 2(pwLc(X) H psi(X)), where pwL(c)( X) <= L(X) and pwL(c)( X) <= c( X). This generalizes results of Bella and Spadaro, as well as Hodel. We show additionally that if X is a Hausdorff linearly Lindelof space such that H psi( X) = omega, then vertical bar X vertical bar <= 2(omega), under the assumption that either 2(

Cardinal inequalities involving the Hausdorff pseudocharacter

Bella, Angelo;
2023-01-01

Abstract

We establish several bounds on the cardinality of a topological space involving the Hausdorff pseudocharacter H psi (X). This invariant has the property psi(c)(X) <= H psi( X) <= chi(X) for a Hausdorff space X. We show the cardinality of a Hausdorff space X is bounded by 2(pwLc(X) H psi(X)), where pwL(c)( X) <= L(X) and pwL(c)( X) <= c( X). This generalizes results of Bella and Spadaro, as well as Hodel. We show additionally that if X is a Hausdorff linearly Lindelof space such that H psi( X) = omega, then vertical bar X vertical bar <= 2(omega), under the assumption that either 2(
2023
Cardinality bounds
Hausdorff pseudocharacter
Topological games
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/615649
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