Limit points which are not sequentially attainable

Autor: D. J. Simanaitis, Otomar Hájek
Rok vydání: 1971
Předmět:
Zdroj: Mathematical Systems Theory. 5:289-291
ISSN: 1433-0490
0025-5661
DOI: 10.1007/bf01694071
Popis: It is well known that limit points need not be sequentially attainable. However, in the familiar examples, the spaces involved have various pathological properti.es (e.g., are badly disconnected, or have high topological type). Here we present a somewhat paradoxical example of this situation, where the space involved contains the real line densely. Actually our space is obtained by adjoining one point, co, to the reals, and the reals form an open dense set. The space supports a natural dynamical system, an extension of the usual real additive system. From a dynamical point of view, the adjoined point is the positive limit set of the additive flow, yet the flow does not approach the point in any sequence of times. It is not known whether the example is universal in any sense, although the construction appears quite natural. We consider first the topological and then the dynamical aspects of the extension.
Databáze: OpenAIRE
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