Related papers: On feebly compact shift-continuous topologies on t…
To any automorphism, $\alpha$, of a totally disconnected, locally compact group, $G$, there is associated a compact, $\alpha$-stable subgroup of $G$, here called the \emph{nub} of $\alpha$, on which the action of $\alpha$ is topologically…
Let $E$ be a Banach space such that $E'$ has the Radon-Nikod\'ym property. The aim of this work is to connect relative weak compactness in the $E$-valued martingale Hardy space $H^{1}(\mu,E)$ to a convex compactness criterion in a weaker…
In this paper, we give the concept of L-fuzzy Semi-Preopen operator in L-fuzzy topological spaces, and use them to score L-fuzzy SP-cmpactnness in L-fuzzy topological spaces. We also study the relationship between L-fuzzy SP-compactness and…
This paper deals with the notion of weak Lawvere-Tierney topology on a topos. Our motivation to study such a notion is based on the observation that the composition of two Lawvere-Tierney topologies is no longer idempotent, when seen as a…
We study computable topological spaces and semicomputable and computable sets in these spaces. In particular, we investigate conditions under which semicomputable sets are computable. We prove that a semicomputable compact manifold $M$ is…
A topologized semilattice $X$ is called complete if each non-empty chain $C\subset X$ has $\inf C$ and $\sup C$ that belong to the closure $C$ of the chain $C$ in $X$. In this paper, we introduce various concepts of completeness of…
We characterize those semilattices that give rise to Boolean spaces on their associated spaces of ultrafilters. The class of 0-disjunctive semilattices, important in the theory of congruence-free inverse semigroups, plays a distinguished…
We prove that the entropy map for countable Markov shifts of finite entropy is upper semi-continuous at ergodic measures. Note that the phase space is non-compact. Applications to systems that can be coded by these shifts, such as positive…
The chiral symmetry at finite lattice spacing of Ginsparg-Wilson fermionic actions constrains the renormalization of the lattice operators; in particular, the topological susceptibility does not require any renormalization, when using a…
We extend Wallman's classic duality from lattice bases to semilattice subbases and from compact to locally closed compact spaces. Moreover, we make this duality functorial via appropriate relational morphisms.
We study shadowing property for random infinite pseudotrajectories of a continuous map $f$ of a compact metric space. For the cases of transitive maps and transitive attractors we prove a dichotomy: either $f$ satisfies shadowing property…
Spin fluctuation-induced superconductivity in quasi-two dimensional organic compounds, \kappa-BEDT-TTF salts, is investigated within a fluctuation exchange (FLEX) approximation using a half-filled Hubbard model with a right-angled isosceles…
We show that for every quasivariety K of structures (where both functions and relations are allowed) there is a semilattice S with operators such that the lattice of quasi-equational theories of K (the dual of the lattice of…
We study Toeplitz operators with respect to a commuting $n$-tuple of bounded operators which satisfies some additional conditions coming from complex geometry. Then we consider a particular such tuple on a function space. The algebra of…
Let $f:X\to X$ be a continuous map on a compact metric space with finite topological entropy. Further, we assume that the entropy map $\mu\mapsto h_\mu(f)$ is upper semi-continuous. It is well-known that this implies the continuity of the…
In this paper, we completely characterize when two dual truncated Toeplitz operators are essentially commuting and when the semicommutator of two dual truncated Toeplitz operators is compact. Our main idea is to study dual truncated…
We use topological consequences of PFA, MA$_{\omega_1}$(S)[S] and PFA(S)[S] proved by other authors to show that normal first countable linearly H-closed spaces with various additionals properties are compact in these models.
Topologies $\tau , \sigma \in \mathop{{\mathrm{Top}}}\nolimits _X$ are bijectively related, in notation $\tau \sim \sigma$, if there are continuous bijections $f: (X, \tau )\rightarrow (X, \sigma )$ and $g: (X, \sigma)\rightarrow (X,…
A dynamical version of the Bourgain-Fremlin-Talagrand dichotomy shows that the enveloping semigroup of a dynamical system is either very large and contains a topological copy of $\beta \N$, or it is a "tame" topological space whose topology…
This paper concerns the compactness and separability properties of the normed Boolean algebras (N.B.A.) with respect to topology generated by a distance equal to the square root of a measure of symmetric difference between two elements. The…