Games are an important tool in mathematics and logic, providing a clear and intuitive understanding of the notions they define or characterize. In particular, since the seminal work of Wadge in the 1970s, game characterizations of classes of functions in Baire space have been a rich area of research, having had significant and far-reaching development by van Wesep, Andretta, Duparc, Motto Ros, ...

One of the main goals of computable analysis is that of formalizing the complexity of theorems from real analysis. In this setting Weihrauch reductions play the role that Turing reductions do in standard computability theory. Via coding, we can transfer computability and topological results from the Baire space ω to any space of cardinality 2א0 , so that e.g. functions over R can be coded as fu...

In a recent paper E. J. McShane [3]2 has given a theorem which is the common core of a variety of results about Baire sets, Baire functions, and convex sets in topological spaces including groups and linear spaces. In general terms his theorem states that if J is a family of open maps defined in one topological space Xi into another, X2, the total image JiS) of a second category Baire set S in ...

A topological space X is Baire if the intersection of any sequence open dense subsets in X. Let $$C_p(X,[0,1])$$ denote all continuous [0, 1]-valued functions on a Tychonoff with topology pointwise convergence. In this paper, we have obtained characterization for function to be separable closed which are $$C^*$$ -embedded. particular, holds normal spaces and, hence, metrizable spaces. Moreover,...