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ABSTRACT. Two countable spaces having no nontrivial convergent sequences are constructed. One space has every point biaccessible (by a countable discrete set), and the other has every point accessible but not biaccessible (by a countable discrete set). It is shown that in a compact T2‐space if a set A is not closed, then there exists a free sequence contained in A whose closure is not contained in A. It follows that in a compact T2‐space of countable tightness, every nonisolated point is biaccessible.
Convergent sequences in iterated ultrapowers as p-compact groups
Convergent sequences in iterated ultrapowers as p-compact groups
3Algebraic structure of countably compact non-torsion Abelian groups of size continuum from selective ultrafilters
Algebraic structure of countably compact non-torsion Abelian groups of size continuum from selective ultrafilters
1Large strongly anti-Urysohn spaces exist
Large strongly anti-Urysohn spaces exist
25Chapter 18 - Efimov's problem
Chapter 18 - Efimov's problem
2S2 and the Fréchet property of free topological groups
S2 and the Fréchet property of free topological groups
10Square of countably compact groups without non-trivial convergent sequences
Square of countably compact groups without non-trivial convergent sequences
22Countably compact groups without non-trivial convergent sequences
We construct, in $\mathsf{ZFC}$, a countably compact subgroup of $2^{\mathfrak{c}}$ without non-trivial convergent sequences, answering an old problem of van Douwen. As a consequence we also prove the existence of two countably compact groups $\mathbb{G}_{0}$ and $\mathbb{G}_{1}$ such that the product $\mathbb{G}_{0} \times \mathbb{G}_{1}$ is not countably compact, thus answering a classical problem of Comfort.
Read more20Spaces which are generated by discrete sets
Spaces which are generated by discrete sets
14A first countable compact space that is not an N∗ image
A first countable compact space that is not an N∗ image
On embeddings of the countable fan space
On embeddings of the countable fan space
4Free Abelian paratopological groups over metric spaces
Free Abelian paratopological groups over metric spaces
On convergent sequences in the Stone space of one Boolean algebra
On convergent sequences in the Stone space of one Boolean algebra
Locally compact, locally countable spaces and random reals
Locally compact, locally countable spaces and random reals
Some dense sets of the Tychonoff cube Ic
Some dense sets of the Tychonoff cube Ic
The analytical properties of the effective static permittivity of a two-component medium
The analytic properties of the dimensionless static effective permittivity f(p, h) of the three-dimensional Rayleigh model as a function of complex variable h are considered. The only singularities of f(p, h) are shown to be first-order poles at real negative h values that form an infinite discrete (denumerable) set. The concentration dependence of the positions of the first four f(p, h) function poles and remainders in them were calculated and presented in the graphic form. An approximate pole-type equation valid over a wide range of concentration p and complex argument h variations was suggested for f(p, h). The results can be used to consistently describe low-frequency dispersion of the effective permittivity of the model under consideration.
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