LOGIKSEMINARIET STOCKHOLM-UPPSALA

Anton Hedin ger ett seminarium med titeln

    Vitali's covering Theorem in constructive mathematics

kl 10.30 - 12.15, onsdagen den 21 april i sal Å4271
(Ångströmlaboratoriet, Uppsala).

Abstract: Vitali's covering Theorem states in its simplest form that if a
closed interval I, in the real numbers, is (Vitali-) covered by a
collection of open intervals V, then for every k>0 there is a finite
subset F of V of pairwise disjoint intervals which cover all of I except a
subset of measure less than k. We show that the Theorem fails in Bishop's
constructive mathematics by giving a recursive counterexample. In fact it
is equivalent to Weak Weak König's Lemma over BISH. Moreover we show that,
under a reasonable interpretation of Vitali covering, the Theorem holds in
the topology of reals in formal topology. The relation to the point-set
result is explained via the concept of spatiality of formal topologies.
The talk is based on joint work with Dr. Hannes Diener.