The Josefson--Nissenzweig theorem and filters on $\omega$

Witold Marciszewski, Damian Sobota

For a free filter $F$ on $\omega$, endow the space $N_F=\omega \cup \{p_F\}$, where $p_F\notin \omega$, with the topology in which every element of $\omega$ is isolated whereas all open neighborhoods of…