Eberly College of Arts and Sciences
n the paper it is proved that if set theory ZFC is consistent then so is the following
ZFC + Martin's Axiom + negation of the Continuum Hypothesis + there exists a 0-dimensional Hausrorff topological space X such that X has net weight nw(X) equal to continuum, but nw(Y)=\omega for every subspace Y of X of cardinality less than continuum. In particular, the countable product X\omega of X is hereditarily separable and hereditarily Lindelof, while X does not have countable net weight. This solves a problem of Arhangel'skii.
Digital Commons Citation
Ciesielski, Krzysztof, "Martin's Axiom and a Regular Topological Space with Uncountable Net Weight Whose Countable Product is Hereditarily Separable and Hereditarily Lindelöf" (1987). Faculty & Staff Scholarship. 819.