More cardinal inequalities in T1/Urysohn spaces

In this paper we provide a partial positive answer to the question 2 in [8]: Do we have |X|≤2L(X)Fa(X)ψ(X), for every T2–space X? Precisely, in Theorem 2.6 we show that |X|≤2L(X)Fa(X)ψθ(X) for Urysohn spaces. Even more, we use cardinal functions recently introduced by Basile, Bonanzinga and Carlson in [4] to generalize some cardinal inequalities; among others, in the Theorem 2.8, we provide a result related with the well known inequality of Hajnal and Juhász: |X|≤2c(X)χ(X); and in the Theorem 2.10, we generalize the inequality |X|≤2wLc(X)χ(X), for any Urysohn space X; due to Ofelia Alas ([1]). Some proofs of the theorems provided in this paper use the elementary submodels technique.