-spaces, perfect spaces and related cardinal characteristics of the continuum
Tom 125 / 2023
Streszczenie
A topological space X is called a Q-space if every subset of X is of type F_\sigma in X. For i\in\{1,2,3\} let \mathfrak q_i be the smallest cardinality of a second-countable T_i-space which is not a Q-space. It is clear that \mathfrak q_1\le\mathfrak q_2\le\mathfrak q_3. For i\in\{1,2\} we prove that \mathfrak q_i is equal to the smallest cardinality of a second-countable T_i-space which is not perfect. Also we prove that \mathfrak q_3 is equal to the smallest cardinality of a submetrizable space which is not a Q-space. Martin’s Axiom implies that \mathfrak q_i=\mathfrak c for all i\in\{1,2,3\}.