So, suppose that i ◦ f : Z → X is continuous. Since for every α, the projection πα : X → Xα is continuous, πα ◦ (i ◦ f) : Z → Xα is continuous. The map πα ◦ (i ◦ f) = iα ◦ (ρα ◦ f). By the universal property of the subspace topology on Yα, the map iα ◦ (ρα ◦ f) being continuous implies ρα ◦ f : Z → Yα is continuous. So, we have a collection of continuous maps: ρα ◦ f : Z → Yα so by the universa...

in this paper, the main results are:a study of the finitely generated mv-algebras of continuous functions from the n-th power of the unit real interval i to i;a study of hopfian mv-algebras; anda category-theoretic study of the map sending an mv-algebra as above to the range of its generators (up to a suitable form of homeomorphism).

Let $nin mathbb{N}$. An additive map $h:Ato B$ between algebras $A$ and $B$ is called $n$-Jordan homomorphism if $h(a^n)=(h(a))^n$ for all $ain A$. We show that every $n$-Jordan homomorphism between commutative Banach algebras is a $n$-ring homomorphism when $n < 8$. For these cases, every involutive $n$-Jordan homomorphism between commutative C-algebras is norm continuous.

We prove that the semigroup operation of a topological semigroup S extends to a continuous semigroup operation on its the Stone-Čech compactification βS provided S is a pseudocompact openly factorizable space, which means that each map f : S → Y to a second countable space Y can be written as the composition f = g ◦ p of an open map p : X → Z onto a second countable space Z and a map g : Z → Y ...

We define pseudocompact topological spaces and prove that every compact space is pseudocompact. We also solve an exercise from [16] p.225 that the for a topological space X the following are equivalent: • Every continuous real map from X is bounded (i.e. X is pseudocompact). • Every continuous real map from X attains minimum. • Every continuous real map from X attains maximum. Finally, for a co...

For two algebras $A$ and $B$, a linear map $T:A longrightarrow B$ is called separating, if $xcdot y=0$ implies $Txcdot Ty=0$ for all $x,yin A$. The general form and the automatic continuity of separating maps between various Banach algebras have been studied extensively. In this paper, we first extend the notion of separating map for module case and then we give a description of a linear se...

A variety of methods are used for speaker adaptation in speech recognition. In some techniques, such as MAP estimation, only the models with available training data are updated. Hence, large amounts of training data are required in order to have significant recognition improvements. In some others, such as MLLR, where several general transformations are applied to model clusters, the results ar...

Approaches for the identification of piecewise affine systems are presented. The identification problem for piecewise affine systems is formulated as a smooth constrained, and a nonsmooth unconstrained optimization problem. The main advantage of the new problem formulations is the fact that no mixed integer problems have to be solved within this method. The feasibility and performance of the pr...