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.
A continuous operator extending fuzzy ultrametrics
We consider the problem of simultaneous extension of fuzzy ultrametrics defined on closed subsets of a complete fuzzy ultrametric space. We construct an extension operator that preserves the operation of pointwise minimum of fuzzy ultrametrics with common domain and an operation which is an analogue of multiplication by a constant defined for fuzzy ultrametrics. We prove that the restriction of the extension operator onto the set of continuous, partial fuzzy ultrametrics is continuous with respect...
A continuous operator extending ultrametrics
The problem of continuous simultaneous extension of all continuous partial ultrametrics defined on closed subsets of a compact zero-dimensional metric space was recently solved by E.D. Tymchatyn and M. Zarichnyi and improvements to their result were made by I. Stasyuk. In the current paper we extend these results to complete, bounded, zero-dimensional metric spaces and to both continuous and uniformly continuous partial ultrametrics.