منابع مشابه
On Point-finiteness in Pointfree Topology
Abstract: In pointfree topology, the point-finite covers introduced by Dowker and Strauss do not behave similarly to their classical counterparts with respect to transitive quasi-uniformities, contrarily to what happens with other familiar types of interior-preserving covers. The purpose of this paper is to remedy this by modifying the definition of Dowker and Strauss. We present arguments to j...
متن کاملOn The Function Rings of Pointfree Topology
The purpose of this note is to compare the rings of continuous functions, integer-valued or real-valued, in pointfree topology with those in classical topology. To this end, it first characterizes the Boolean frames (= complete Boolean algebras) whose function rings are isomorphic to a classical one and then employs this to exhibit a large class of frames for which the functions rings are not o...
متن کاملStrong 0-dimensionality in Pointfree Topology
Classically, a Tychonoff space is called strongly 0-dimensional if its Stone-Čech compactification is 0-dimensional, and given the familiar relationship between spaces and frames it is then natural to call a completely regular frame strongly 0-dimensional if its compact completely regular coreflection is 0-dimensional (meaning: is generated by its complemented elements). Indeed, it is then seen...
متن کاملC- and C -quotients in Pointfree Topology
We generalize a major portion of the classical theory of Cand C embedded subspaces to pointfree topology, where the corresponding notions are frame Cand C -quotients. The central results characterize these quotients and generalize Urysohns Extension Theorem, among others. The proofs require calculations in CL, the archimedean f -ring of frame maps from the topology of the reals into the frame ...
متن کاملRings of Real Functions in Pointfree Topology
This paper deals with the algebra F(L) of real functions of a frame L and its subclasses LSC(L) and USC(L) of, respectively, lower and upper semicontinuous real functions. It is well-known that F(L) is a lattice-ordered ring; this paper presents explicit formulas for its algebraic operations which allow to conclude about their behaviour in LSC(L) and USC(L). As applications, idempotent function...
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ژورنال
عنوان ژورنال: Applied Categorical Structures
سال: 2006
ISSN: 0927-2852,1572-9095
DOI: 10.1007/s10485-006-9039-2