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.

The familiar Intermediate Value Theorem of elementary calculus says that if a real valued function f is continuous on the interval [a, b] ⊆ R then it takes each value between f(a) and f(b). As our next result shows, the critical fact is that the domain of f , the interval [a, b], is a connected space, for the theorem generalizes to real-valued functions on any connected space. The Intermediate ...

We consider known expressions for the eigenvalue of Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation in N=4 super Yang-Mills theory as a real valued function two variables. define new functions complex conjugate variables that have definite complexity analogous to weight nested harmonic sums. argue those span general space BFKL at any order perturbation theory.

We develop the flow analog of the classical Yosida adjunction between spaces and archimedean lattice-ordered groups with strong unit. A product of this development is the flow counterpart of the classical compactification of a space. We characterize those flows which are compactifiable, i.e., dense subflows of a compact flow. Finally, we exhibit a duality between the compactifications of a give...

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.

We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact  (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we pr...

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