Topology Proceedings 43 (2014) pp. 69-82: C and C* among intermediate rings

Topology Proceedings 45 (2015) pp. 301-313: Characterizing C(X) among intermediate C-rings on X

Let X be a completely regular topological space. An intermediate ring is a ring A(X) of continuous functions satisfying C∗(X) ⊆ A(X) ⊆ C(X). We give a characterization of C(X) in terms of extensions of functions in A(X) to real-compactifications of X. We also give equivalences of properties involving the closure in the real-compactifications of X of zero-sets in X; we use these equivalences to ...

Linear Topological Division Algebras

1. R. F. Arens, A topology for spaces of transformations, Ann. of Math. vol. 47 (1946) pp. 480-495. 2. R. F. Arens ond J. L. Kelley, Characterizations of the space of continuous functions over a compact Hausdorff space, To be published in Trans. Amer. Math. Soc. 3. S. Banach, Théorie des opérations linéaires, Warsaw, 1932. 4. G. Birkhoff, Lattice theory, Amer. Math. Soc. Colloquium Publications...

z-Ideals and zº-Ideals in the Factor Rings of C(X)

Topology Proceedings 5 (1980) pp. 59-69: SEPARABILITY IN NEARLY COMPACT SYMMETRIZABLE SPACES

Mappings to Realcompactifications

In this paper, we introduce and study  a mapping from the collection of all  intermediate rings of $C(X)$ to the collection of all  realcompactifications of $X$ contained in $beta X$. By establishing the relations between this mapping and its converse,  we give a different approach to the main statements of De et. al. Using these, we provide different answers to the   four basic questions...