Closure operators on O-categories.
Coarse dimensions and partitions of unity.
Gromov and Dranishnikov introduced asymptotic and coarse dimensions of proper metric spaces via quite different ways. We define coarse and asymptotic dimension of all metric spaces in a unified manner and we investigate relationships between them generalizing results of Dranishnikov and Dranishnikov-Keesling-Uspienskij.
Coarse structures and group actions
The main results of the paper are: Proposition 0.1. A group G acting coarsely on a coarse space (X,𝓒) induces a coarse equivalence g ↦ g·x₀ from G to X for any x₀ ∈ X. Theorem 0.2. Two coarse structures 𝓒₁ and 𝓒₂ on the same set X are equivalent if the following conditions are satisfied: (1) Bounded sets in 𝓒₁ are identical with bounded sets in 𝓒₂. (2) There is a coarse action ϕ₁ of a group G₁ on (X,𝓒₁) and a coarse action ϕ₂ of a...
Codensity and binding categories
Coequalizers in the generalized algebraic categories
Cofibrations and the realization of non-deterministic automata
Cofinalities of complete Boolean algebras.
Cogeneration and minimal realization (Preliminary communication)
Coherence and Embedding of Algebras.
Coherent spaces constructively
Cohomology Theories In Synthetic Differential Geometry.
Colimits in free categories
Commutative monoids all of whose principal ideals are projective.
Commutative semigroup cohomology.
Compact topologies on locally presentable categories
Compactness and Löwenheim-Skolem properties in categories of pre-institutions
The abstract model-theoretic concepts of compactness and Löwenheim-Skolem properties are investigated in the "softer" framework of pre-institutions [18]. Two compactness results are presented in this paper: a more informative reformulation of the compactness theorem for pre-institution transformations, and a theorem on natural equivalences with an abstract form of the first-order pre-institution. These results rely on notions of compact transformation, which are introduced as arrow-oriented generalizations...
Complete subobjects of fuzzy sets over -algebras
A subobjects structure of the category - of -fuzzy sets over a complete -algebra is investigated, where an -fuzzy set is a pair such that is a set and is a special map. Special subobjects (called complete) of an -fuzzy set which can be identified with some characteristic morphisms are then investigated. It is proved that some truth-valued morphisms , are characteristic morphisms of complete subobjects.
Completely normal locales
Completely regular spaces
We conduct an investigation of the relationships which exist between various generalizations of complete regularity in the setting of merotopic spaces, with particular attention to filter spaces such as Cauchy spaces and convergence spaces. Our primary contribution consists in the presentation of several counterexamples establishing the divergence of various such generalizations of complete regularity. We give examples of: (1) a contigual zero space which is not weakly regular and is not a Cauchy...
Completion as reflection