On linear functorial operators extending pseudometrics
نویسندگان
چکیده
For a functor F ⊃ Id on the category of metrizable compacta, we introduce a conception of a linear functorial operator T = {TX : Pc(X) → Pc(FX)} extending (for each X) pseudometrics from X onto FX ⊃ X (briefly LFOEP for F ). The main result states that the functor SP G of G-symmetric power admits a LFOEP if and only if the action of G on {1, . . . , n} has a one-point orbit. Since both the hyperspace functor exp and the probability measure functor P contain SP 2 as a subfunctor, this implies that both exp and P do not admit LFOEP.
منابع مشابه
The Functorial Relations between Alexandrov Fuzzy Topologies and Upper Approximation Operators
In this paper, we investigate functorial relations between Alexandrov fuzzy topologies and upper approximation operators in complete residuated lattices. We present some examples. AMS Subject Classification: 03E72, 03G10, 06A15, 06F07, 54A40
متن کاملRobust similarity between hypergraphs based on valuations and mathematical morphology operators
This article aims at connecting concepts of similarity, hypergraph and mathematical morphology. We introduce new measures of similarity and study their relations with pseudometrics defined on lattices. More precisely, based on various lattices that can be defined on hypergraphs, we propose some similarity measures between hypergraphs based on valuations and mathematical morphology operators. We...
متن کاملGeneralized Metrics and Their Relevance for FCA and Closure Operators
We provide an approach to generalized metrics that covers various concepts of distance. In particular, we consider functorial maps which are weakly positive. Here, we focus on the supermodular case which generalizes dimension functions. We give a lattice-theoretically based construction for supermodular functorial maps, which generalize those arising from Dempster-Shafer-Theory. Within this fra...
متن کاملCoalgebraic Behavioral Metrics
We study different behavioral metrics, such as those arising from both branching and linear-time semantics, in a coalgebraic setting. Given a coalgebra $\alpha\colon X \to HX$ for a functor $H \colon \mathrm{Set}\to \mathrm{Set}$, we define a framework for deriving pseudometrics on $X$ which measure the behavioral distance of states. A crucial step is the lifting of the functor $H$ on $\mathrm{...
متن کاملA comparative study of fuzzy norms of linear operators on a fuzzy normed linear spaces
In the present paper, we rst modify the concepts of weakly fuzzy boundedness, strongly fuzzy boundedness, fuzzy continuity, strongly fuzzy continuity and weakly fuzzy continuity. Then, we try to nd some relations by making a comparative study of the fuzzy norms of linear operators.
متن کامل