We explore almost-normality in Isbell-Mr\'owka spaces and some related concepts. use forcing to provide an example of almost-normal not normal almost disjoint family, the concept semi-normality spaces, define strongly $(\aleph_0, <\mathfrak c)$-separated families prove generic existence completely separable c)$-almost assuming $\mathfrak s=\mathfrak c$ b=\mathfrak c$. also a Tychonoff pseudocom...

The Ostrowski theorem in question is that an additive function bounded (above, say) on a set T of positive measure is continuous. In the converse direction, recall that a topological space T is pseudocompact if every function continuous on T is bounded. Thus theorems of ‘converse Ostrowski’type relate to ‘additive (pseudo)compactness’. We give a di¤erent characterization of such sets, in terms ...