A Generalization of the Strict Topology.
A generating family for the Freudenthal compactification of a class of rimcompact spaces
For X a Tikhonov space, let F(X) be the algebra of all real-valued continuous functions on X that assume only finitely many values outside some compact subset. We show that F(X) generates a compactification γX of X if and only if X has a base of open sets whose boundaries have compact neighborhoods, and we note that if this happens then γX is the Freudenthal compactification of X. For X Hausdorff and locally compact, we establish an isomorphism between the lattice of all subalgebras of and the...
A new semilattice of function algebras and its Boolean form on a lattice of groups.
A note on continuous linear mappings between function spaces
A note on rings of continuous functions.
A note on the algebraic de Morgan's law
A subspace of and its connexions with the maximal ring of quotients
About solutions of a functional equation.
Adequate families of sets and Corson compacts
Adequate families of sets and function spaces
Alcune caratterizzazioni di una sottoalgebra di e compattificazioni ad essa associate
Algebraic characterization of finite (branched) coverings
Every continuous map X → S defines, by composition, a homomorphism between the corresponding algebras of real-valued continuous functions C(S) → C(X). This paper deals with algebraic properties of the homomorphism C(S) → C(X) in relation to topological properties of the map X → S. The main result of the paper states that a continuous map X → S between topological manifolds is a finite (branched) covering, i.e., an open and closed map whose fibres are finite, if and only if the induced homomorphism...
Algebraic properties of rings of continuous functions
This paper is devoted to the study of algebraic properties of rings of continuous functions. Our aim is to show that these rings, even if they are highly non-noetherian, have properties quite similar to the elementary properties of noetherian rings: we give going-up and going-down theorems, a characterization of z-ideals and of primary ideals having as radical a maximal ideal and a flatness criterion which is entirely analogous to the one for modules over principal ideal domains.
Algebras of real-valued uniform maps
An example of a Ф-algebra whose uniform closure is a ring of continuous functions
Approximation of with countable subsets of and calibers of the space
A-realcompact spaces.
Relations between homomorphisms on a real function algebra and different properties (such as being inverse-closed and closed under bounded inversion) are studied.
Banach Lattices with Locally Compact Representation Spaces.
can sometimes determine without being realcompact
As usual will denote the ring of real-valued continuous functions on a Tychonoff space . It is well-known that if and are realcompact spaces such that and are isomorphic, then and are homeomorphic; that is determines. The restriction to realcompact spaces stems from the fact that and are isomorphic, where is the (Hewitt) realcompactification of . In this note, a class of locally compact spaces that includes properly the class of locally compact realcompact spaces is exhibited...
Characterizing the interval and circle by composition of functions