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A strong generalized topological space is an ordered pair $\mathbf{X}=\langleX, \mathcal{T}\rangle$ such that $X$ is a set and $\mathcal{T}$ is a collectionof subsets of $X$ such that $\emptyset, X\in \mathcal{T}$ and $\mathcal{T}$ isstable under arbitrary unions. A necessary and sufficient condition for astrong generalized topological space $\mathbf{X}$ to satisfy Urysohn's lemma orits appropriate variant is shown in $\mathbf{ZF}$. Notions of a U-normal and aneffectively normal generalized topological space are introduced. It is observedthat, in $\mathbf{ZF}+\mathbf{DC}$, every U-normal generalized topologicalspace satisfies Urysohn's lemma. It is shown that every effectively normalgeneralized topological space satisfies Csasz\'ar's modification of Urysohn'sLemma. A $\mathbf{ZF}$- example of a strong generalized topological normalspace which satisfies the Tietze-Urysohn Extension Theorem and fails to satisfyUrysohn's Lemma is shown.

On Urysohn's Lemma for generalized topological spaces in ZF