Intersection properties of open sets, II
Intersection properties of open sets, II
I. Juhász, Zs. Nagy, L. Soukup, Z. Szentmiklóssy:
Intersection properties of open sets, II
A topological space is called P_2 (P_3, P_{<\omega}) if and only
if it does not contain two (three, finitely many) uncountable open sets
with empty intersection. We show that
- there are 0-dimensional P_{<\omega} spaces of size 2^\omega,
- there are compact P_{<\omega} spaces of size \omega_1,
- the existence of a \Psi-like examples for (ii) is independent of ZFC,
- it is consistent that 2^\omega is as large as you wish but
every first countable (and so every compact) P_2 space has
cardinality \le\omega_1.