This is an announcement for the paper "Quotient normed cones" by Oscar Valero. Abstract: Given a normed cone $(X,p)$ and a subcone $Y,$ we construct and study the quotient normed cone $(X/Y,\tilde{p})$ generated by $Y$. In particular we characterize the bicompleteness of $(X/Y,\tilde{p})$ in terms of the bicompleteness of $(X,p),$ and prove that the dual quotient cone $((X/Y)^{*},\|\cdot \|_{\tilde{p},u})$ can be identified as a distinguished subcone of the dual cone $(X^{*},\|\cdot \|_{p,u})$. Furthermore, some parts of the theory are presented in the general setting of the space $CL(X,Y)$ of all continuous linear mappings from a normed cone $(X,p)$ to a normed cone $(Y,q),$ extending several well-known results related to open continuous linear mappings between normed linear spaces. Archive classification: Functional Analysis; General Topology Mathematics Subject Classification: 54E35; 54E50; 54E99; 54H11 Remarks: 17 pages The source file(s), mat01.cls: 37258 bytes, mathtimy.sty: 20 bytes, pm2745new.tex: 58553 bytes, is(are) stored in gzipped form as 0607619.tar.gz with size 26kb. The corresponding postcript file has gzipped size 61kb. Submitted from: o.valero@uib.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0607619 or http://arXiv.org/abs/math.FA/0607619 or by email in unzipped form by transmitting an empty message with subject line uget 0607619 or in gzipped form by using subject line get 0607619 to: math@arXiv.org.