  We propose a continuous time model for financial markets with proportional
transactions costs and a continuum of risky assets. This is motivated by bond
markets in which the continuum of assets corresponds to the continuum of
possible maturities. Our framework is well adapted to the study of no-arbitrage
properties and related hedging problems. In particular, we extend the
Fundamental Theorem of Asset Pricing of Guasoni, R\'asonyi and L\'epinette
(2012) which concentrates on the one dimensional case. Namely, we prove that
the Robust No Free Lunch with Vanishing Risk assumption is equivalent to the
existence of a Strictly Consistent Price System. Interestingly, the presence of
transaction costs allows a natural definition of trading strategies and avoids
all the technical and un-natural restrictions due to stochastic integration
that appear in bond models without friction. We restrict to the case where
exchange rates are continuous in time and leave the general c\`adl\`ag case for
further studies.
