Let C(X,Z), C(X,Q) and C(X) denote the l-groups of integer-valued, rationalvalued and real-valued continuous functions on a topological space X, respectively. Characterizations are given for the extensions C(X,Z) 6 C(X,Q) 6 C(X) to be rigid, major, and dense.

Let Sβ := {z ∈ C : | Im z| < β} be a strip in the complex plane. For fixed integer r ≥ 0 let Hr ∞,β denote the class of 2π-periodic functions f , which are analytic in Sβ and satisfy |f(r)(z)| ≤ 1 in Sβ . Denote by Hr,R ∞,β the subset of functions from Hr ∞,β that are real-valued on the real axis. Given a function f ∈ Hr ∞,β , we try to recover f(ζ) at a fixed point ζ ∈ R by an algorithm A on t...

For realcompact spaces X and Y we give a complete description of the linear biseparating maps between spaces of vector-valued continuous functions on X and Y , where special attention is paid to spaces of vector-valued bounded continuous functions. These results are applied to describe the linear isometries between spaces of vector-valued bounded continuous and uniformly continuous functions.

For a Tychonoff space $X$, we denote by $C_p(X)$ the of all real-valued continuous functions on $X$ with topology pointwise convergence.&nbsp; We study functional characterization covering property Hurewicz.