Domain Representations of Topological Spaces (extended Abstract)
نویسنده
چکیده
A domain representation of a topological space X is a function usually a quotient map from a subset of a domain onto X Several di erent classes of domain representations are introduced and studied It is investigated when it is possible to build domain representations from existing ones It is for example discussed whether there exists a natural way to build a domain representation of a product of topological spaces from given domain rep resentations of the factors It is shown that any topological space has a domain representation These domain representations are very large However smaller do main representations are also constructed for large classes of spaces For example each second countable regular Hausdor space has a domain representation with a countable base Domain representations of functions and function spaces are also studied
منابع مشابه
Σ 0 α - Admissible Representations ( Extended Abstract )
We investigate a hierarchy of representations of topological spaces by measurable functions that extends the traditional notion of admissible representations common to computable analysis. Specific instances of these representations already occur in the literature (for example, the naive Cauchy representation of the reals and the “jump” of a representation), and have been used in investigating ...
متن کاملdominating subset and representation graph on topological spaces
Let a topological space. An intersection graph on a topological space , which denoted by , is an undirected graph which whose vertices are open subsets of and two vertices are adjacent if the intersection of them are nonempty. In this paper, the relation between topological properties of and graph properties of are investigated. Also some classifications and representations for the graph ...
متن کاملAdmissible Domain Representations of Topological Spaces
In this paper we consider admissible domain representations of topological spaces. A domain representation D of a space X is λ-admissible if, in principle, all other λ-based domain representations E of X can be reduced to D via a continuous function from E to D. We present a characterisation theorem of when a topological space has a λ-admissible and κ-based domain representation. We also prove ...
متن کاملDomain representations of topological spaces
A domain representation of a topological space X is a function, usually a quotient map, from a subset of a domain onto X . Several di erent classes of domain representations are introduced and studied. It is investigated when it is possible to build domain representations from existing ones. It is, for example, discussed whether there exists a natural way to build a domain representation of a p...
متن کاملTopology-based representations for motion planning and grasping
topology-based representations that describe the interactions between 1D curves using their original configurations were proposed for motion synthesis (Edmond and Komura, 2009; Tamei et al., 2011) and for classifying paths into homotopy groups (Bhattacharya et al., 2011). In (Edmond and Komura, 2009), a representation based on the Gauss Linking Integral was suggested to generate winding movemen...
متن کامل