Linearly Ordered Topological Spaces and Weak Domain Representability
نویسنده
چکیده
It is well known that domain representable spaces, that is topological spaces which are homeomorphic to the space of maximal elements of some domain, must be Baire. In this paper it is shown that every linearly ordered topological space (LOTS) is homeomorphic to an open dense subset of a weak domain representable space. This means that weak domain representable spaces need not be Baire. MR Classifications: primary = 54H99; secondary = 54F05, 54E52, 06B35,
منابع مشابه
Numerical Representability of Ordered Topological Spaces with Compatible Algebraic Structure
We analyze the numerical representability of total preorders defined on semitopological real algebras through continuous order-preserving real-valued functions that are also additive and multiplicative. The results obtained are used to interpret important concepts arising in Social Choice theory.
متن کاملRepresentability of Certain Function Spaces
LetCp(X) be the space of all continuous real-valued functions on a space X , with the topology of pointwise convergence. In this paper we show thatCp(X) is not domain representable unless X is discrete for a class of spaces that includes all pseudo-radial spaces and all generalized ordered spaces. This is a first step toward our conjecture that if X is completely regular, then Cp(X) is domain r...
متن کامل$L-$ordered Fuzzifying Convergence Spaces
Based on a complete Heyting algebra, we modify the definition oflattice-valued fuzzifying convergence space using fuzzy inclusionorder and construct in this way a Cartesian-closed category, calledthe category of $L-$ordered fuzzifying convergence spaces, in whichthe category of $L-$fuzzifying topological spaces can be embedded.In addition, two new categories are introduced, which are called the...
متن کاملTopological Properties of Spaces Ordered by Preferences
In this paper, we analyze the main topological properties of a relevant class of topologies associated with spaces ordered by preferences (asymmetric, negatively transitive binary relations). This class consists of certain continuous topologies which include the order topology. The concept of saturated identification is introduced in order to provide a natural proof of the fact that all these s...
متن کاملWeak hyper semi-quantales and weak hypervalued topological spaces
The purpose of this paper is to construct a weak hyper semi-quantale as a generalization of the concept of semi-quantale and used it as an appropriate hyperlattice-theoretic basis to formulate new lattice-valued topological theories. Based on such weak hyper semi-quantale, we aim to construct the notion of a weak hypervalued-topology as a generalized form of the so-called lattice-valued t...
متن کامل