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1 results

  • ON METRIZATION OF UNIONS OF FUNCTION SPACES ON DIFFERENT INTERVALS

  • TALEB ALKURDI, SANDER C. HILLE, ONNO VAN GAANS
  • Journal:
    Journal of the Australian Mathematical Society / Volume 92 / Issue 3 / June 2012
    Published online by Cambridge University Press:
    04 March 2013, pp. 281-297
    Print publication:
    June 2012
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  • This paper investigates a class of metrics that can be introduced on the set consisting of the union of continuous functions defined on different intervals with values in a fixed metric space, where the union ranges over a family of intervals. Its definition is motivated by the Skorohod metric(s) on càdlàg functions. We show what is essential in transferring the ideas employed in the latter metric to our setting and obtain a general construction for metrics in our case. Next, we define the metric space where elements are sequences of functions from the above mentioned set. We provide conditions that ensure separability and completeness of the constructed metric spaces.