Free algebras and automata realizations in the language of categories
Free algebras, input processes and free monads
Free, iteratively closed categories of complete lattices
From where do figurative algebras come ?
Frontiers of infinite trees
Full embeddings into the categories of Boolean algebras
Full embeddings with a given restriction
Function spaces and adjoints.
Functionally Hausdorff spaces
Functions characterized by images of sets
For non-empty topological spaces X and Y and arbitrary families ⊆ and we put =f ∈ : (∀ A ∈ )(f[A] ∈ . We examine which classes of functions ⊆ can be represented as . We are mainly interested in the case when is the class of all continuous functions from X into Y. We prove that for a non-discrete Tikhonov space X the class (X,ℝ) is not equal to for any ⊆ and ⊆ (ℝ). Thus, (X,ℝ) cannot be characterized by images of sets. We also show that none of the following classes of...
Functor of extension in Hilbert cube and Hilbert space
It is shown that if Ω = Q or Ω = ℓ 2, then there exists a functor of extension of maps between Z-sets in Ω to mappings of Ω into itself. This functor transforms homeomorphisms into homeomorphisms, thus giving a functorial setting to a well-known theorem of Anderson [Anderson R.D., On topological infinite deficiency, Michigan Math. J., 1967, 14, 365–383]. It also preserves convergence of sequences of mappings, both pointwise and uniform on compact sets, and supremum distances as well as uniform continuity,...
Functorial algebras and automata
Functorial concepts of complexity for finite automata.
Functorial polymorphism and semantic parametricity
Functorial properties of the lattice of functional semi-norms.
Functors on locally finitely presented additive categories
Fundamental pro-groupoids and covering projections
We introduce a new notion of covering projection E → X of a topological space X which reduces to the usual notion if X is locally connected. We use locally constant presheaves and covering reduced sieves to find a pro-groupoid π crs (X) and an induced category pro (π crs (X), Sets) such that for any topological space X the category of covering projections and transformations of X is equivalent to the category pro (π crs (X), Sets). We also prove that the latter category is equivalent to pro (π CX,...
Fundamental pushout toposes.
Funktoren auf Kategorien von Banachräumen.