A note on Finiteness and Boundedness in Cartesian Products of Discrete and Well-Ordered Sets, Application to Transition Systems
Gerard Memmi
Abstract
In this short note, we prove that any closed interval in a well-ordered and discrete space is finite. The coincidence between finiteness and boundedness can then be established for transition systems where the state space is well-ordered and discrete. Finally, this result is also proven when the state space is a Cartesian product of d discrete and well-ordered sets.
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