To clarify Damian's post:-
Dumb car chargers use a constant 14.4v and are unsuitable for continuous use on any battery as gassing and electrolyte loss will be caused.
Other dumb chargers, like on-board caravan power supplies, limit their voltage to 13.8v maximum to prevent gassing. These can be used continuously but will only charge a battery to about 90% and won't prevent sulphation.
Smart (intelligent) chargers start with a high 14.4v / 14.8v charge but then reduce the voltage to around 13.0v to maintain a 100% charged battery. When necessary the smart charger will go through it's cycles again. The higher initial charge reduces sulphation, some smart chargers have an anti-sulphation phase which almost eliminates it.
Most caravans have dumb on-board power suppliers but some manufacturers are starting to fit dual stage supply/chargers.
It's not as simple as saying "anything over 13.8v is too much" - it all depends on the charger. 13.5v is an irrelevant figure anyway.