We adopt the following rules: n, m are elements of N, T is a non empty topological space, and M , M1, M2 are non empty metric spaces. The following propositions are true: (1) Let A, B, S, T be topological spaces, f be a function from A into S, and g be a function from B into T . Suppose that (i) the topological structure of A = the topological structure of B, (ii) the topological structure of S...

Cadastral space may be the object of legal, geometric and topological analyses. Topological aspects, which are least recognized by the users, are deployed by IT specialists in the process of developing analytical applications. This study attempts to analyze the theoretical aspects of cadastral-topological space. Algebraic topology delivers a new approach by using a single mathematical formula t...

Three experiments on tachistoscopic perception of visual stimuli demonstrate that the visual system is sensitive to global topological properties. The results indicate that extraction of global topological properties is a basic factor in perceptual organization.

Topological defects are produced during phase transitions in the very early Universe. They arise in most unified theories of strong, weak and electromagnetic interactions. These lectures focus on the role of topological defects in cosmology, with particular emphasis on the models of structure formation based on defects. The role of topological defects in baryogenesis is also reviewed. ⋆ Based o...

The human memory system is an integration of three distributed memory systems associated with respective autonomous organic systems; the perceptual system that takes care of sensory input from the environment, the conscious system that performs deliberate decision making, and the unconscious system that carries out action selections in the environment. The memory system works as a memory compon...

Quantitative structure-retention relationships (QSRRs) are used to correlate paper chromatographic retention factors of disperse dyes with theoretical molecular descriptors. A data set of 23 compounds with known RF values was used. The genetic algorithm-multiple linear regression analysis (GA-MLR) with three selected theoretical descriptors was obtained. The stability and predictability of the ...

In this paper, we propose a topological metaphor for computations: computing consists in moving through a path in a data space and making some elementary computations along this path. This idea underlies an experimental declarative programming language called mgs. mgs introduces the notion of topological collection: a set of values organized by a neighborhood relationship. The basic computation...

It is well-known that classical two-dimensional topological field theories are in one-to-one correspondence with commutative Frobenius algebras. An important extension of classical two-dimensional topological field theories is provided by open-closed two-dimensional topological field theories. In this paper we extend open-closed two-dimensional topological field theories to nonorientable surfac...

We define and study a quantale-valued Wijsman structure on the hyperspace of all non-empty closed sets of a quantale-valued metric space. We show its admissibility and that the metrical coreflection coincides with the quantale-valued Hausdorff metric and that, for a metric space, the topological coreflection coincides with the classical Wijsman topology. We further define an index of compactnes...