Finite trace observations induce the Cantor topology on infinite traces while simulation observations generate a finer topology, with a general theorem equating open sets to finitely verifiable properties.
Kleijnen (1995):Verification and validation of simulation models.European Journal of Operational Research82(1), pp
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A Topological Framework for Finite Behavioural Observations and Verification
Finite trace observations induce the Cantor topology on infinite traces while simulation observations generate a finer topology, with a general theorem equating open sets to finitely verifiable properties.