Mathematics Commons^™

Martin's Axiom And A Regular Topological Space With Uncountable Net Weight Whose Countable Product Is Hereditarily Separable And Hereditarily Lindelöf, Krzysztof Ciesielski

Faculty & Staff Scholarship

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.