Exponential fields and Conway’s omega-map

EXPONENTIAL MAP OF A CLASS OF TOP SPACES

Real closed exponential fields

In an extended abstract [20], Ressayre considered real closed exponential fields and integer parts that respect the exponential function. He outlined a proof that every real closed exponential field has an exponential integer part. In the present paper, we give a detailed account of Ressayre’s construction. The construction becomes canonical once we fix the real closed exponential field R, a re...

Invariant Subspaces and the Exponential Map

Bounded operators with no non-trivial closed invariant subspace have been constructed by P. Enflo [6]. In fact, there exist bounded operators on the space 1 with no non-trivial closed invariant subset [12]. It is still unknown, however, if such operators exist on reflexive Banach spaces, or on the separable Hilbert space. The main result of this note (Theorem 1) asserts that the existence of an...

N ov 2 00 8 EXPONENTIAL ALGEBRAICITY IN EXPONENTIAL FIELDS

I give an algebraic proof that the exponential algebraic closure operator in an exponential field is always a pregeometry, and show that its dimension function satisfies a weak Schanuel property. A corollary is that there are at most countably many essential counterexamples to Schanuel’s conjecture.

exponential map of a class of top spaces

0