O riešení niektorých nerozhodnutelných topologických problémov
On a certain class of -structures. I
On a certain class of -structures. II
On a question of
In this short article we answer the question posed in Ghadermazi M., Karamzadeh O.A.S., Namdari M., On the functionally countable subalgebra of , Rend. Sem. Mat. Univ. Padova 129 (2013), 47–69. It is shown that is isomorphic to some ring of continuous functions if and only if is functionally countable. For a strongly zero-dimensional space , this is equivalent to say that is functionally countable. Hence for every -space it is equivalent to pseudo--compactness.
On Bicompact Extensions of Tychonoff Spaces.
On bijectivity of the canonical transformation
On butterfly-points in , Tychonoff products and weak Lindelöf numbers
Let be the Tychonoff product of -many Tychonoff non-single point spaces . Let be a point in the closure of some whose weak Lindelöf number is strictly less than the cofinality of . Then we show that is not normal. Under some additional assumptions, is a butterfly-point in . In particular, this is true if either or and is infinite and not countably cofinal.
On character of points in the Higson corona of a metric space
We prove that for an unbounded metric space , the minimal character of a point of the Higson corona of is equal to if has asymptotically isolated balls and to otherwise. This implies that under a metric space of bounded geometry is coarsely equivalent to the Cantor macro-cube if and only if and . This contrasts with a result of Protasov saying that under CH the coronas of any two asymptotically zero-dimensional unbounded metric separable spaces are homeomorphic.
On cohomological dimension of a space and its Stone-Čech compactification
On compactification of absolute retracts
On compactifications with continua as remainders
On Compactifying a Topological Space by Adding a Finite Number of Points
On compactifying semigroups.
On continuous extensions.
On -compactifications and -compactifiable spaces.
On Eberlein compactifications of metrizable spaces
We prove that, for every finite-dimensional metrizable space, there exists a compactification that is Eberlein compact and preserves both the covering dimension and weight.
On extension of the group operation over the Čech-Stone compactification
The convolution of ultrafilters of closed subsets of a normal topological group is considered as a substitute of the extension onto of the group operation. We find a subclass of ultrafilters for which this extension is well-defined and give some examples of pathologies. Next, for a given locally compact group and its dense subgroup , we construct subsets of β algebraically isomorphic to . Finally, we check whether the natural mapping from β onto β is a homomorphism with respect to the extension...
On extensions of fuzzy topologies
On factorization of maps through τX
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.