‎It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$‎. ‎Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology‎, ‎which is compact by the Banach--Alaoglu theorem‎. ‎We prove that the compact Hausdorff space $X$ can ...

In this paper we introduce a new definition of a lattice fuzzy topology which is a generalization of Lowen’s fuzzy topology and show that the category of Lowen’s fuzzy topological spaces is a bireflective full subcategory of the category of lattice fuzzy topological spaces.

In this paper, following the ideas of (continuous) t-norm and interval numbers, a concept of (continuous) interval-valued t-norm is proposed. Based on the interval-valued fuzzy set and the continuous interval-valued t-norm, we propose a notion of interval-valued fuzzy metric space, which is a generalization of fuzzy metric space in the sense of George and Veeramani [Fuzzy Sets and Systems 64 (1...

Topology and geometry are essential to our understanding of modern physics, underlying many foundational concepts from high-energy theories, quantum information, and condensed-matter physics. In condensed-matter systems, a wide range of phenomena stem from the geometry of the band eigenstates, which is encoded in the matrix-valued Wilson line for general multiband systems. Using an ultracold ga...

The variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and many-valued logic, lattice theory, game theory, and topology. One source of this richness is the inherent non-monotonicity of its negation, something that does not have close parallels with the machinery of other programming paradigms. Nonetheless, much of the work on logic p...

ACVF is the theory of non-trivially valued algebraically closed valued f ields. This theory is the model companion of the theory of valued fields. ACVF does not have elimination of imaginaries in the home sort (the valued field sort). Nevertheless, Haskell, Hrushovski, and Macpherson in [2] were able to find a collection of “geometric sorts” in which elimination of imaginaries holds. Let K be a...

The aim of the present paper is to define the localization BL-algebra of a BL-algebra A with respect to a topology F on A. In the last part of the paper is proved that the maximal BL-algebra of quotients (defined in [5]) and the BLalgebra of fractions relative to a ∧-closed system (defined in [4]) are BL-algebras of localization. A remarkable construction in ring theory is the localization ring...

Multi-Valued Symbolic Model-Checking: Fairness, Counter-Examples, Running Time Arie Gurfinkel Master of Science Graduate Department of Computer Science University of Toronto 2003 Multi-valued model-checking is an effective technique for reasoning about systems with incomplete or inconsistent information. In particular, it is well suited for reasoning about abstract, partial, and feature-based s...

In order to investigate a many valued logical system whose proportional value is given in a lattice, in 1993 Y. Xu [12] first established the lattice implication algebra by combining lattice and implication algebra, and explored many useful structures. The ideal theory serves a vital function for the development of lattice implication algebras. Y. Xu, Y.B. Jun and E.H. Roh [6] introduced the no...

We give geometric characterisations of patch and Lawson topologies in the context of predicative point-free topology using the constructive notion of located subset. We present the patch topology of a stably locally compact formal topology by a geometric theory whose models are the points of the given topology that are located, and the Lawson topology of a continuous lattice by a geometric theo...