Geodesic
Reflecting character and pseudocharacter
Commentationes Mathematicae Universitatis Carolinae, Tome 56 (2015) no. 3, pp. 365-376.

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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 $\mathrm{CH}$.
DOI : 10.14712/1213-7243.2015.127
Classification : 54A25, 54A35, 54D20, 54D30
Keywords: cardinal function; character; pseudocharacter; reflection theorem; compact spaces; Lindelöf spaces; continuum hypothesis 
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Junqueira, Lucia R.; Levi, Alberto M. E. Reflecting character and pseudocharacter. Commentationes Mathematicae Universitatis Carolinae, Tome 56 (2015) no. 3, pp. 365-376. doi : 10.14712/1213-7243.2015.127. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.127/

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