On extensions of uniformly continuous Banach-space-valued mappings
On factorization of maps through τX
On families of Lindelöf and related subspaces of
We consider the families of all subspaces of size ω₁ of (or of a compact zero-dimensional space X of weight ω₁ in general) which are normal, have the Lindelöf property or are closed under limits of convergent ω₁-sequences. Various relations among these families modulo the club filter in are shown to be consistently possible. One of the main tools is dealing with a subspace of the form X ∩ M for an elementary submodel M of size ω₁. Various results with this flavor are obtained. Another tool used...
On finest unitary extensions of topological monoids
We prove that the Wyler completion of the unitary Cauchy space on a given Hausdorff topological 5 monoid consisting of the underlying set of this monoid and of the family of unitary Cauchy filters on it, is a T2-topological space and, in the commutative case, an abstract monoid containing the initial one.
On finite powers of countably compact groups
We will show that under for each there exists a group whose -th power is countably compact but whose -th power is not countably compact. In particular, for each there exists and a group whose -th power is countably compact but the -st power is not countably compact.
On Frolík’s characterization of class
On FU()-spaces and -sequential spaces
Following Kombarov we say that is -sequential, for , if for every non-closed subset of there is such that and . This suggests the following definition due to Comfort and Savchenko, independently: is a FU()-space if for every and every there is a function such that . It is not hard to see that ( denotes the Rudin–Keisler order) every -sequential space is -sequential every FU()-space is a FU()-space. We generalize the spaces to construct examples of -sequential...
On function spaces of compact subspaces of Σ-products of the real line
On functions preserving almost radiality and their relations to radial and pseudo-radial spaces
On functors from compact to Banach algebras
On functors of finite degree and -metrizable bicompact spaces.
On fuzzy semi-pre-generalized closed sets.
On games of Topsoe.
On generalizations of regular-Lindelöf spaces.
On generalized -closed sets.
On Hausdorff compactifications of non-locally compact spaces.
On Hausdorff Quotients of Spaces and Magill's Theorem.
On hereditarily normal topological groups
We investigate hereditarily normal topological groups and their subspaces. We prove that every compact subspace of a hereditarily normal topological group is metrizable. To prove this statement we first show that a hereditarily normal topological group with a non-trivial convergent sequence has -diagonal. This implies, in particular, that every countably compact subspace of a hereditarily normal topological group with a non-trivial convergent sequence is metrizable. Another corollary is that under...
On hereditarily separable Hausdorff spaces in the constructible universe
On hereditarily α-Lindelöf and α-separable spaces, II