  The paper investigates the variation of the spectrum of operators in infinite
dimensional Banach spaces. In particular, it is shown that the spectrum
function is Borel from the space of bounded operators on a separable Banach
space; equipped with the strong operator topology, into the Polish space of
compact subsets of the closed unit disc of the complex plane; equipped with the
Hausdorff topology. Remarks and results are given when other topologies are
used.
