A Lindelöf space X such that is normal but not paracompact
A little more on the product of two pseudocompact spaces
A local version of the generalized retract theorem of Ważewski with applications in the theory of partial differential equations of first order
A locally connected non-movable continuum that fails to separate
A local-nonglobal Hurewicz fibration
A López-Escobar theorem for metric structures, and the topological Vaught conjecture
We show that a version of López-Escobar’s theorem holds in the setting of model theory for metric structures. More precisely, let denote the Urysohn sphere and let Mod(,) be the space of metric -structures supported on . Then for any Iso()-invariant Borel function f: Mod(,) → [0,1], there exists a sentence ϕ of such that for all M ∈ Mod(,) we have . This answers a question of Ivanov and Majcher-Iwanow. We prove several consequences, for example every orbit equivalence relation of a Polish group...
A Mapping Theorem on Aleph-spaces
A matrix formalism for conjugacies of higher-dimensional shifts of finite type
We develop a natural matrix formalism for state splittings and amalgamations of higher-dimensional subshifts of finite type which extends the common notion of strong shift equivalence of ℤ⁺-matrices. Using the decomposition theorem every topological conjugacy between two -shifts of finite type can thus be factorized into a finite chain of matrix transformations acting on the transition matrices of the two subshifts. Our results may be used algorithmically in computer explorations on topological...
A maximal chain approach to topology and order.
A Maximality Principle On Ordered Metric Spaces.
A Measurable Selection Theorem for Compact-Valued Maps.
A metatheorem for fixed point theories
A metric on the space of projections admitting nice isometries
Motivated by the concept of separation between propositions in quantum logic, we introduce the so-called separation metric or Santos metric on the space of all projections in a Hilbert space. We show that the resulting metric space has only "nice" surjective isometries. On the nontrivial projections they are all unitarily or antiunitarily equivalent to the identity or to taking the orthogonal complement. We relate this result to Wigner's classical theorem on the form of quantum mechanical symmetry...
A metric tangential calculus.
A metrizable completely regular ordered space
We construct a completely regular ordered space such that is an -space, the topology of is metrizable and the bitopological space is pairwise regular, but not pairwise completely regular. (Here denotes the upper topology and the lower topology of .)
A metrization theorem
A metrization theorem for countably compact spaces
A metrization theorem for developable spaces
A metrization theorem for the product of ordered continua
A minimal regular ring extension of C(X)
Let G(X) denote the smallest (von Neumann) regular ring of real-valued functions with domain X that contains C(X), the ring of continuous real-valued functions on a Tikhonov topological space (X,τ). We investigate when G(X) coincides with the ring of continuous real-valued functions on the space , where is the smallest Tikhonov topology on X for which and is von Neumann regular. The compact and metric spaces for which are characterized. Necessary, and different sufficient, conditions...