The first known continuous extension result was obtained by Lebesgue in 1907. In 1915, Tietze published his famous theorem generalising Lebesgue's from the plane to general metric spaces. He constructed an explicit formula involving distance function on space. Thereafter, several authors contributed other formulas. present paper, we show that all these constructions also preserve uniform contin...

We study the space of all continuous fuzzy-valued functions  from a space $X$ into the space of fuzzy numbers $(mathbb{E}sp{1},dsb{infty})$  endowed with the pointwise convergence topology.   Our results generalize the classical ones for  continuous real-valued functions.   The field of applications of this approach seems to be large, since the classical case  allows many known devices to be fi...

In the present paper, among other results, a decomposition formula is given for the w-bounded continuous negative definite functions of a topological *-semigroup S with a weight function w into a proper H*-algebra A in terms of w-bounded continuous positive definite A-valued functions on S. A generalization of a well-known result of K. Harzallah is obtained. An earlier conjecture of the author ...