The cardinal characteristic for relative γ-sets

The cardinal characteristic for relative γ-sets

For X a separable metric space define p(X) to be the smallest cardinality of a subset Z of X which is not a relative γset in X, i.e., there exists an ω-cover of X with no γ-subcover of Z. We give a characterization of p(2) and p(ω) in terms of definable free filters on ω which is related to the pseudo-intersection number p. We show that for every uncountable standard analytic space X that eithe...

2 5 M ay 2 00 4 The cardinal characteristic for relative γ - sets

For X a separable metric space define p(X) to be the smallest cardinality of a subset Z of X which is not a relative γset in X, i.e., there exists an ω-cover of X with no γ-subcover of Z. We give a characterization of p(2) and p(ω) in terms of definable free filters on ω which is related to the psuedointersection number p. We show that for every uncountable standard analytic space X that either...

Cardinal invariants of monotone and porous sets

A metric space (X, d) is monotone if there is a linear order < on X and a constant c such that d(x, y) 6 c d(x, z) for all x < y < z in X. We investigate cardinal invariants of the σ-ideal Mon generated by monotone subsets of the plane. Since there is a strong connection between monotone sets in the plane and porous subsets of the line, plane and the Cantor set, cardinal invariants of these ide...

Cardinal Numbers and Finite Sets 1 Karol

The articles [21], [10], [24], [17], [26], [6], [27], [2], [9], [11], [1], [25], [7], [8], [22], [19], [5], [15], [12], [20], [16], [14], [18], [13], [3], [23], and [4] provide the terminology and notation for this paper. For simplicity, we use the following convention: x, x1, x2, y, z, X ′ denote sets, X, Y denote finite sets, n, k, m denote natural numbers, and f denotes a function. Next we s...

Γ-sets and Γ-continuous Functions