Correction to the paper: Covering by special Cantor sets
Correction to the paper: “Set-like equivalence and inner and outer cuts”
Correction to the paper "Two classes of measures''
Corrections : «Les dérivations analytiques»
Correspondance de Fréchet (1907-1926) et son apport à la théorie de la dimension (avec 3 lettres de Brouwer à Baire)
Correspondence between interval -equivalences and -functions
Corrigendum à l'article "Sur la construction de certaines MS-algèbres" (Port. Math., 39(1-4) (1980), 489-496)
Cotorsion-free algebras as endomorphism algebras in - the discrete and topological cases
The discrete algebras over a commutative ring which can be realized as the full endomorphism algebra of a torsion-free -module have been investigated by Dugas and Göbel under the additional set-theoretic axiom of constructibility, . Many interesting results have been obtained for cotorsion-free algebras but the proofs involve rather elaborate calculations in linear algebra. Here these results are rederived in a more natural topological setting and substantial generalizations to topological...
Countable Compact Scattered T₂ Spaces and Weak Forms of AC
We show that: (1) It is provable in ZF (i.e., Zermelo-Fraenkel set theory minus the Axiom of Choice AC) that every compact scattered T₂ topological space is zero-dimensional. (2) If every countable union of countable sets of reals is countable, then a countable compact T₂ space is scattered iff it is metrizable. (3) If the real line ℝ can be expressed as a well-ordered union of well-orderable sets, then every countable compact zero-dimensional T₂ space...
Countable dense homogeneity and λ-sets
We show that all sufficiently nice λ-sets are countable dense homogeneous (𝖢𝖣𝖧). From this fact we conclude that for every uncountable cardinal κ ≤ 𝔟 there is a countable dense homogeneous metric space of size κ. Moreover, the existence of a meager in itself countable dense homogeneous metric space of size κ is equivalent to the existence of a λ-set of size κ. On the other hand, it is consistent with the continuum arbitrarily large that every 𝖢𝖣𝖧 metric space has size either ω₁ or 𝔠. An...
Countable homogeneous coloured partial orders [Book]
Countable inductive definitions in AST
Countable modules
Countable nondeterminism and logics of programs: fair-wellfoundedness of while-programs with nondeterministic assignments in the logic ALNA
Countable partitions of the sets of points and lines
The following theorem is proved, answering a question raised by Davies in 1963. If is a partition of the set of lines of , then there is a partition such that whenever . There are generalizations to some other, higher-dimensional subspaces, improving recent results of Erdős, Jackson Mauldin.
Countable splitting graphs
A graph is called splitting if there is a 0-1 labelling of its vertices such that for every infinite set C of natural numbers there is a sequence of labels along a 1-way infinite path in the graph whose restriction to C is not eventually constant. We characterize the countable splitting graphs as those containing a subgraph of one of three simple types.
Countable sums and products of Loeb and selective metric spaces
We investigate the role that weak forms of the axiom of choice play in countable Tychonoff products, as well as countable disjoint unions, of Loeb and selective metric spaces.
Countably metacompact spaces in the constructible universe
We present a construction from ♢* of a first countable, regular, countably metacompact space with a closed discrete subspace that is not a . In addition some nonperfect spaces with σ-disjoint bases are constructed.
Counterexamples in minimally generated Boolean algebras
Counting measure for Kuratowski finite parts and decidability