Approximation Spaces of Type-Free Sets
We present an approximation space (U;R) which is an infinite (hypercontinuum) solution to the domain equation U ≈ C(R), the family of elementary subsets of U. Thus U is a universe of type-free sets and R is the relation of indiscernibility with respect to membership in other type-free sets. R thus associates a family [u]R of elementary subsets with u ∈ U, whence (U;R) induces an generalized approximation space (U; c : U → U; i : U → U); where c(u) = ∪[u]R and i(u) = ∩[u]R.
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