A completion functor for Cauchy groups.
A completion of is a field
We define various ring sequential convergences on and . We describe their properties and properties of their convergence completions. In particular, we define a convergence on by means of a nonprincipal ultrafilter on the positive prime numbers such that the underlying set of the completion is the ultraproduct of the prime finite fields . Further, we show that is sequentially precompact but fails to be strongly sequentially precompact; this solves a problem posed by D. Dikranjan.
A condition equivalent to covering dimension for normal spaces
A condition under which 2-homogeneity and representability are the same in continua
A Cone of Inhomogeneous Second-Order Polynomials.
A conglomerate of exponential supercategories of the category of finitely generated topological spaces.
A connected locally connected countable space which is almost regular
A connected subset of the plane
A connection between multiplication in C(X) and the dimension of X
Let X be a compact Hausdorff topological space. We show that multiplication in the algebra C(X) is open iff dim X < 1. On the other hand, the existence of non-empty open sets U,V ⊂ C(X) satisfying Int(U· V) = ∅ is equivalent to dim X > 1. The preimage of every set of the first category in C(X) under the multiplication map is of the first category in C(X) × C(X) iff dim X ≤ 1.
A construction of a CW-decomposition of s-cubes which are manifolds
A construction of a Fréchet-Urysohn space, and some convergence concepts
Some strong versions of the Fréchet-Urysohn property are introduced and studied. We also strengthen the concept of countable tightness and generalize the notions of first-countability and countable base. A construction of a topological space is described which results, in particular, in a Tychonoff countable Fréchet-Urysohn space which is not first-countable at any point. It is shown that this space can be represented as the image of a countable metrizable space under a continuous pseudoopen mapping....
A construction of noncontractible simply connected cell-like two-dimensional Peano continua
Using the topologist sine curve we present a new functorial construction of cone-like spaces, starting in the category of all path-connected topological spaces with a base point and continuous maps, and ending in the subcategory of all simply connected spaces. If one starts from a noncontractible n-dimensional Peano continuum for any n > 0, then our construction yields a simply connected noncontractible (n + 1)-dimensional cell-like Peano continuum. In particular, starting from the circle 𝕊¹,...
A construction of the Gleason space
A construction of the projective modification for a closure-set of a presheaf
A constructive “Closed subgroup theorem” for localic groups and groupoids
A constructive proof of the Tychonoff's theorem for locales
A continuation method for weakly contractive mappings under the interior condition.
A continuation method for weakly Kannan maps.
A continuous, constructive solution to Hilbert's 17th problem.
A continuous dependence of fixed points of -contractive mappings in uniform spaces
The main purpose of the present paper is to established conditions for a continuous dependence of fixed points of -contractive mappings in uniform spaces. An application to nonlinear functional differential equations of neutral type have been made.