The universal semilattice compactification of a semigroup.
The universal separable metric space of Urysohn and isometric embeddings thereof in Вanach spaces
This paper is an investigation of the universal separable metric space up to isometry U discovered by Urysohn. A concrete construction of U as a metric subspace of the space C[0,1] of functions from [0,1] to the reals with the supremum metric is given. An answer is given to a question of Sierpiński on isometric embeddings of U in C[0,1]. It is shown that the closed linear span of an isometric copy of U in a Banach space which contains the zero of the Banach space is determined up to linear isometry....
The utility of empty inverse limits
The variational principle
The variational principle of fixed point theorems in certain fuzzy topological spaces
The main purpose of this paper is to introduce the concept of -type fuzzy topological spaces. Further variational principle and Caristi’s fixed point theorem have been extended in the -type fuzzy topological spaces.
The volume near the zeroes of a smooth function.
The weak Radon-Nikodym property in Banach spaces
The Whitehead and the Smale theorems in shape theory [Book]
The Whitehead Theorem in the theory of shapes
The Williams conjecture is false for irreducible subshifts.
The Williams conjecture is false for irreducible subshifts.
The -completion of a lattice ordered group
The -property in
The -property of a Riesz space (real vector lattice) is: For each sequence of positive elements of , there is a sequence of positive reals, and , with for each . This condition is involved in studies in Riesz spaces of abstract Egoroff-type theorems, and of the countable lifting property. Here, we examine when “” obtains for a Riesz space of continuous real-valued functions . A basic result is: For discrete , has iff the cardinal , Rothberger’s bounding number. Consequences and...
The σ-ideal of closed smooth sets does not have the covering property
We prove that the σ-ideal I(E) (of closed smooth sets with respect to a non-smooth Borel equivalence relation E) does not have the covering property. In fact, the same holds for any σ-ideal containing the closed transversals with respect to an equivalence relation generated by a countable group of homeomorphisms. As a consequence we show that I(E) does not have a Borel basis.
Theorem on signatures
Théorème d'approximation et espaces de Hopf.
Théorème d'Ascoli et application aux groupes topologiques localement compacts en analyse non standard
Théorêmes de point fixe pour les applications contractantes et anticontractantes.
Theorems fo Stone-Weierstrass Type for Non-Compact Spaces.
Theorems on common fixed points