Fibrewise exponential laws in a quasitopos
Filter convergence via sequential convergence
Finite commutative monoids of open maps
Firm reflections generated by complete metric spaces
Frames in Priestley's duality
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,...
Higher-dimensional categories with finite derivation type.
Homotopic pullbacks, Lax pullbacks, and exponentiability
Homotopy preserving functors
Homotopy transition cocycles.
Inequilogical spaces, directed homology and noncommutative geometry.
Initial Morphisms and Monomorphisms.
Least and largest initial completions. I.
Liftings of Stone's monadicity to spaces and the duality between the calculi of inverse and direct images
Linking the closure and orthogonality properties of perfect morphisms in a category
We define perfect morphisms to be those which are the pullback of their image under a given endofunctor. The interplay of these morphisms with other generalisations of perfect maps is investigated. In particular, closure operator theory is used to link closure and orthogonality properties of such morphisms. A number of detailed examples are given.
Local enrichments of categories
Model theoretic approach to concrete categories
Monoidal closed structures for topological spaces : counter-example to a question of Booth and Tillotson