# zbMATH — the first resource for mathematics

Weakly Whyburn spaces of continuous functions on ordinals. (English) Zbl 1121.54011
Summary: We characterize those ordinals $$\xi$$ for which $$C_p(\xi)$$ is a weakly Whyburn space. As a byproduct we obtain the coincidence of the Fréchet property and the Whyburn one on $$C_p(\xi)$$.

##### MSC:
 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets) 54C35 Function spaces in general topology 54B99 Basic constructions in general topology 46E10 Topological linear spaces of continuous, differentiable or analytic functions
Full Text:
##### References:
 [1] Arhangel’skiı̆, A.V., Topological function spaces, Math. appl., 78, (1992), Kluwer Academic Dordrecht [2] Bella, A.; Yaschenko, I.V., On AP and WAP spaces, Comm. mat. univ. carolin., 40, 531-536, (1999) · Zbl 1010.54040 [3] Gerlits, J.; Nagy, Z.; Szenntmiklossy, Z., Some convergence properties in function spaces, (), 211-222 [4] K. Kunen, Set Theory, An Introduction to Independence Results, North-Holland, Amsterdam · Zbl 0443.03021 [5] F. Obersnel, Some notes on weakly Whyburn spaces, Topology Appl. (2000), in press
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.