This is an announcement for the paper "The triangle of operators, topologies, bornologies" by Ngai-Ching Wong. Abstract: 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. Archive classification: Functional Analysis; Operator Algebras Mathematics Subject Classification: 47L20, 46A03, 46A11, 46A17 Remarks: 33 pages The source file(s), triangle05_ArXiV.tex: 98877 bytes, is(are) stored in gzipped form as 0506183.gz with size 27kb. The corresponding postcript file has gzipped size 124kb. Submitted from: wong@math.nsysu.edu.tw The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0506183 or http://arXiv.org/abs/math.FA/0506183 or by email in unzipped form by transmitting an empty message with subject line uget 0506183 or in gzipped form by using subject line get 0506183 to: math@arXiv.org.