# zbMATH — the first resource for mathematics

Three cardinal functions similar to net weight. (English) Zbl 0694.54004
An important and useful cardinal function for a topological space is that of weight, namely, the minimum cardinal for a base of open sets. Net weight is similar to weight, except that “base” members need not be open. The authors look at three cardinal functions which are slight variations of net weight called pseudonet weight, weak net weight, and weak pseudonet weight. These are similar to but generally smaller than net weight. They look at how these cardinal functions relate to hereditary Lindelöf degree, hereditary density, and spread, and study their behavior under products.

##### MSC:
 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
Full Text:
##### References:
 [1] Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna. Tom 47. [Mathematics Library. Vol. 47]. Ryszard Engelking, General topology, PWN — Polish Scientific Publishers, Warsaw, 1977. Translated from the Polish by the author; Monografie Matematyczne, Tom 60. [Mathematical Monographs, Vol. 60]. [2] D. H. Fremlin, Consequences of Martin’s axiom, Cambridge University Press, Cambridge, 1984. · Zbl 0551.03033 [3] A. Hajnal and I. Juhász, On hereditarily $$\alpha$$-Lindelöf and hereditarily $$\alpha$$-separable spaces, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 9 (1968), 115-124. · Zbl 0172.24601 [4] R. Hodel, Cardinal functions. I, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 1 – 61. [5] I. Juhász, K. Kunen, and M. E. Rudin, Two more hereditarily separable non-Lindelöf spaces, Canad. J. Math. 28 (1976), no. 5, 998 – 1005. · Zbl 0336.54040 · doi:10.4153/CJM-1976-098-8 · doi.org [6] A. J. Ostaszewski, On countably compact, perfectly normal spaces, J. London Math. Soc. (2) 14 (1976), no. 3, 505 – 516. · Zbl 0348.54014 · doi:10.1112/jlms/s2-14.3.505 · doi.org [7] Phillip Zenor, Hereditary \?-separability and the hereditary \?-Lindelöf property in product spaces and function spaces, Fund. Math. 106 (1980), no. 3, 175 – 180. · Zbl 0454.54011
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.