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Keywords:
cardinal function; character; pseudocharacter; reflection theorem; compact spaces; Lindelöf spaces; continuum hypothesis
cardinal function; character; pseudocharacter; reflection theorem; compact spaces; Lindelöf spaces; continuum hypothesis
Summary:
We say that a cardinal function $\phi$ reflects an infinite cardinal $\kappa$, if given a topological space $X$ with $\phi (X) \geq \kappa$, there exists $Y\in [X]^{\leq \kappa}$ with $\phi (Y)\geq \kappa$. We investigate some problems, discussed by Hodel and Vaughan in Reflection theorems for cardinal functions, Topology Appl. 100 (2000), 47--66, and Juhász in Cardinal functions and reflection, Topology Atlas Preprint no. 445, 2000, related to the reflection for the cardinal functions character and pseudocharacter. Among other results, we present some new equivalences with $\mathrm{CH}$.
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