Abstract: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 {\it Reflection theorems for cardinal functions\/}, Topology Appl. {\bf 100} (2000), 47--66, and Juh\'asz in {\it 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 $\mathrm{CH}$.
Keywords: cardinal function; character; pseudocharacter; reflection theorem; compact spaces; Lindel\"of spaces; continuum hypothesis
DOI: DOI 10.14712/1213-7243.2015.127
AMS Subject Classification: 54A25 54A35 54D20 54D30