  In this paper, a general framework is developed for continuous-time financial
market models defined from simple strategies through conditional topologies
that avoid stochastic calculus and do not necessitate semimartingale models. We
then compare the usual no-arbitrage conditions of the literature, e.g. the
usual no-arbitrage conditions NFL, NFLVR and NUPBR and the recent AIP
condition. With appropriate pseudo-distance topologies, we show that they hold
in continuous time if and only if they hold in discrete time. Moreover, the
super-hedging prices in continuous time coincide with the discrete-time
super-hedging prices, even without any no-arbitrage condition.
