A common fixed-point theorem in 2 non-Archimedean Menger PM-space for R-weakly commuting maps of type (P).
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 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 contraction theorem in fuzzy metric spaces.
A contraction theorem in Menger probabilistic metric spaces.
A convergence criterion for monotone global dynamical systems.
A converse of the Arsenin–Kunugui theorem on Borel sets with σ-compact sections
Let f be a Borel measurable mapping of a Luzin (i.e. absolute Borel metric) space L onto a metric space M such that f(F) is a Borel subset of M if F is closed in L. We show that then is a set for all except countably many y ∈ M, that M is also Luzin, and that the Borel classes of the sets f(F), F closed in L, are bounded by a fixed countable ordinal. This gives a converse of the classical theorem of Arsenin and Kunugui. As a particular case we get Taĭmanov’s theorem saying that the image of...
A Converse To A Generalized Banach Contraction Principle
A countable dense homogeneous set of reals of size ℵ₁
We prove there is a countable dense homogeneous subspace of ℝ of size ℵ₁. The proof involves an absoluteness argument using an extension of the logic obtained by adding predicates for Borel sets.
A countably compact, separable space which is not absolutely countably compact
We construct a space having the properties in the title, and with the same technique, a countably compact topological group which is not absolutely countably compact.
A counter example on common periodic points of functions.
A counterexample on a theorem by Khojasteh, Goodarzi, and Razani.
A counterexample to a Fedorenko statement.
A counterexample to a theorem of Argyros
A counterexample to “An extension of Gregus fixed point theorem”.
A counterexample to ”Common fixed point theorem in probabilistic quasi-metric spaces".