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In this paper, we consider the notion of quasi-multipliers to the general topological algebra setting, not necessarily normed or locally convex. We discuss the quasi-uniform and quasi-strong operator topologies on the algebra QM(A) of all bilinear and jointly continuous quasi-multipliers on A and study their various properties. [ABSTRACT FROM AUTHOR]

Abstract: Let G denote a locally compact Hausdorff group and be the space of all bounded complex-valued regular Borel measures on G. In this paper, we define two strict topologies on and study various properties of these topologies such as metrizability, barrelledness and completeness. We also determine the dual space of and consider various continuity properties for the convolution product on under these topologies. [Copyright &y& Elsevier]

Data such as real and complex numbers, discrete and continuous time data streams, waveforms, scalar and vector fields, and many other functions, are fundamental for many kinds of computation. In the theory of data, such data types are modelled using topological, or metric, many-sorted algebras and continuous homomorphisms. A theory of such topological data types is needed to answer the general questions:Such a theory seems to be in its infancy: there are many approaches to computability theory on general and specific spaces, and few approaches to specification theory. In some earlier papers, we have studied the questions 1 and 2 with the needs of data type theory in mind, and built a bridge between computations and specifications to try to answer 3. In this paper, we extend and combine several of our results, to prove new theorems thatA technical issue is the localisation of uniform continuity using exhaustions of open sets. We use specifications composed of conditional equations, inequalities and, for convenience, new exhaustion primitives, that define functions uniquely up to isomorphism. [Copyright &y& Elsevier]