A note on $σ$-discrete and massive spaces

Rok, strany: 2004, 43 - 56

Some cardinality properties of $σ$-discrete and massive spaces are considered. These spaces were essentially used in the study of the problem on the existence of $ω$-primitives [Z. Dusyński, Z. Grande and S. P. Ponomarev: On the $ω$-primitive, Math. Slovaca 51 (2001), 469–476], [J. Ewert and S. P. Ponomarev: $ω$-primitives on $σ$-discrete metric spaces, Tatra Mt. Math. Publ. 24 (2002), 13–37], [J. Ewert and S. P. Ponomarev: On the existence of $ω$-primitives on arbitrary metric spaces, Math. Slovaca 3 (2003), 51–57], [J.Ewert and S. P. Ponomarev: Oscillation and $ω$-primitives, Real Anal. Exchange 26 (2001–2002), 687–702]. It is shown, in particular, that unlike metric spaces, a topological space which is not locally $σ$-discrete, need not contain a massive subspace. Moreover, a locally $σ$-discrete topological space need not be $σ$-discrete, and a massive topological space may contain a discrete subset of cardinality greater than the remaining set (in contrast with the case of metric spaces). Some other cardinality properties of the mentioned spaces, in particular under GCH or MA, are also discussed.

ISO 690:

Ponomarev, S. 2004. A note on $σ$-discrete and massive spaces. In Tatra Mountains Mathematical Publications, vol. 28, no.1, pp. 43-56. 1210-3195.

APA:

Ponomarev, S. (2004). A note on $σ$-discrete and massive spaces. Tatra Mountains Mathematical Publications, 28(1), 43-56. 1210-3195.