Compactifiers in extension constructions for reachability problems with constraints of asymptotic nature
- 27 Downloads
A reachability problem with constraints of asymptotic nature is considered in a topological space. The properties of a rather general procedure that defines an extension of the problem are studied. In particular, we specify a rule that transforms an arbitrary extension scheme (a compactifier) into a similar scheme with the property that the continuous extension of the objective operator of the reachability problem is homeomorphic. We show how to use this rule in the case when the extension is realized in the ultrafilter space of a broadly understood measurable space. This version is then made more specific for the case of an objective operator defined on a nondegenerate interval of the real line.
Keywordsattraction set topological space ultrafilter quotient space
Unable to display preview. Download preview PDF.
- 3.N. N. Krasovskii, Theory of Motion Control (Nauka, Moscow, 1968) [in Russian].Google Scholar
- 7.A. V. Bulinskii and A. N. Shiryaev, The Theory of Random Processes (Fizmatlit, Moscow, 2005) [in Russian].Google Scholar
- 11.N. Bourbaki, General Topology (Hermann, Paris, 1940; Nauka, Moscow, 1968).Google Scholar
- 15.P. S. Aleksandrov, Introduction to the Theory of Sets and General Topology (Editorial URSS, Moscow, 2004) [in Russian].Google Scholar
- 16.A. G. Chentsov, “Tier mappings and ultrafilter-based transformations,” Trudy Inst. Mat. Mekh. UrO RAN 18 (4), 298–314 (2012).Google Scholar
- 17.A. G. Chentsov, “An abstract reachability problem: “Purely asymptotic” version,” Trudy Inst. Mat. Mekh. UrO RAN 21 (2), 289–305 (2015).Google Scholar
- 20.A. G. Chentsov, “On one example of representing the ultrafilter space for an algebra of sets,” Trudy Inst. Mat. Mekh. 17 (4), 293–311 (2011).Google Scholar