  This paper discusses two common techniques in functional analysis: the
topological method and the bornological method. In terms of Pietsch's operator
ideals, we establish the equivalence of the notions of operators, topologies
and bornologies. The approaches in the study of locally convex spaces of
Grothendieck (via Banach space operators), Randtke (via continuous seminorms)
and Hogbe-Nlend (via convex bounded sets) are compared.
