Metric transitivity and integer valued functions

Integer-valued continuous functions

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Integer-valued definable functions

We present a dichotomy, in terms of growth at infinity, of analytic functions definable in the real exponential field which take integer values at natural number inputs. Using a result concerning the density of rational points on curves definable in this structure, we show that if a function f : [0,∞) → R is such that f(N) ⊆ Z, then either sup|x̄|≤r f(x̄) grows faster than exp(r), for some δ > 0,...

Countable composition closedness and integer-valued continuous functions in pointfree topology

‎For any archimedean$f$-ring $A$ with unit in whichbreak$awedge‎ ‎(1-a)leq 0$ for all $ain A$‎, ‎the following are shown to be‎ ‎equivalent‎: ‎ ‎1‎. ‎$A$ is isomorphic to the $l$-ring ${mathfrak Z}L$ of all‎ ‎integer-valued continuous functions on some frame $L$‎. 2‎. ‎$A$ is a homomorphic image of the $l$-ring $C_{Bbb Z}(X)$‎ ‎of all integer-valued continuous functions‎, ‎in the usual se...

Best approximation by integer-valued functions

Given an integer function f , the problem is to find its best uniform approximation from a set K of integervalued bounded functions. Under certain conditions on K , the best extremal (maximal or minimal) approximation is identified. Furthermore, the operator mapping f to its extremal best approximation is shown to be Lipschitzian with some constant C or optimal Lipschitzian having the smallest ...

A Remark on Eqtjipartitioning and Metric Transitivity