منابع مشابه
Strong 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...
متن کاملExtended Real Functions in Pointfree Topology
In pointfree topology, a continuous real function on a frame L is a map L(R) → L from the frame of reals into L. The discussion of continuous real functions with possibly infinite values can be easily brought to pointfree topology by replacing the frame L(R) with the frame of extended reals L ( R ) (i.e. the pointfree counterpart of the extended real line R = R ∪ {±∞}). One can even deal with a...
متن کاملOn 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...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2018
ISSN: 0166-8641
DOI: 10.1016/j.topol.2018.06.007