We prove that the locally convex space $ C_ {p}(X) $ of continuous real-valued functions on
a Tychonoff space $ X $ equipped with the topology of pointwise convergence is …

We consider the closed subspace of ℓ∞ generated by c 0 and the characteristic functions of
elements of an uncountable, almost disjoint family A of infinite subsets of N. This Banach …

Almost disjoint families of true cardinality $\mathfrak c $ are used to produce an example of
a mildly-normal non-partly-normal $\Psi $-space and a quasi-normal non-almost-normal …

We give examples of $ n $-sequentially compact spaces that are not $(n+ 1) $-sequentially
compact under several assumptions. We improve results from Kubis and Szeptycki by …

For many years, there have been conducting research (eg, by Bergelson, Furstenberg,
Kojman, Kubiś, Shelah, Szeptycki, Weiss) into sequentially compact spaces that are, in a …

The paper consists of two parts. In the first part (Sections 3–7) we examine various kinds of
(non) pathological submeasures that are considered in the literature, whereas the second …

We explore almost-normality in Isbell-Mrówka spaces and some related concepts. We use
forcing to provide an example of an almost-normal not normal almost disjoint family, explore …

We prove pseudocompactness of a Tychonoff space X and the space of Radon probability
measures on it with the weak topology under the condition that the Stone–Čech …

We introduce a generalization of sequential compactness using barriers on $\omega $
extending naturally the notion introduced in arxiv: 2111.14729. We improve results from …

We consider uncountable almost disjoint families of subsets of N, the Johnson-
Lindenstrauss Banach spaces (XA,‖‖∞) induced by them, and their natural equivalent …