In [5] the following question was put: are there any maximal n.d. sets in ${\omega }^{*}$? Already in [9] the negative answer (under MA) to this question was obtained. Moreover, in [9] it was shown that no $P$-set can be maximal n.d. In the present paper the notion of a maximal n.d. $P$-set is introduced and it is proved that under CH there is no such a set in ${\omega }^{*}$. The main results are Theorem 1.10 and especially Theorem 2.7(ii) (with Example in Section 3) in which the problem of the existence of maximal n.d. $P$-sets...

We prove that a separable Hausdor_ topological space X containing a cocountable subset homeomorphic to [0, ω1] admits no separately continuous mean operation and no diagonally continuous n-mean for n ≥ 2.

We prove that the statement: "there is a Corson compact space with a non-separable Radon measure" is equivalent to a number of natural statements in set theory.

According to Comfort, Raczkowski and Trigos-Arrieta, a dense subgroup D of a compact abelian group G determines G if the restriction homomorphism Ĝ → D̂ of the dual groups is a topological isomorphism. We introduce four conditions on D that are necessary for it to determine G and we resolve the following question: If one of these conditions holds for every dense (or $G_{\delta }$-dense) subgroup D of G, must G be metrizable? In particular, we prove (in ZFC) that a compact abelian group determined by all its...

In this paper we show that a minimal space in which compact subsets are closed is countably compact. This answers a question posed in [1].

$\mathrm{𝐒𝐩𝐅𝐢}$ is the category of spaces with filters: an object is a pair $(X,ℱ)$, $X$ a compact Hausdorff space and $ℱ$ a filter of dense open subsets of $X$. A morphism $f(Y,𝒢)\to (X,ℱ)$ is a continuous function $fY\to X$ for which $f^{-1}\left(F\right)\in 𝒢$ whenever $F\in ℱ$. This category arises naturally from considerations in ordered algebra, e.g., Boolean algebra, lattice-ordered groups and rings, and from considerations in general topology, e.g., the theory of the absolute and other covers, locales, and frames, though we shall specifically address only one of these...

In this paper, we study the monotone meta-Lindelöf property. Relationships between monotone meta-Lindelöf spaces and other spaces are investigated. Behaviors of monotone meta-Lindelöf $GO$-spaces in their linearly ordered extensions are revealed.

We consider the question of when $X_M=X$, where $X_M$ is the elementary submodel topology on X ∩ M, especially in the case when $X_M$ is compact.