Indiscernibility in topologies of finitely observable properties
In this article we are interested in dealing formally with the natural intuition of indiscernibility in finite "observations" over frames whose points are finite and infinite strings of elements under prefix ordering. In this case we deal with the well-known space 2* described as a spatial locale of finite and infinite strings of binary bits in [12] in which we prove from a classical point of view and based on a result in [9] that only finitely many elements in its Scott topology can be distinguished. Further, we offer a nonstandard (IST) version of indiscernibility in 2*(omega) by means of an approximate equality and consequently of the topological halos of its standard points based on a relevant work by T. Sari [8].
finitely observable property boundedly observable property internal set theory nonstandard theories standard set topological proximity total boundedness