Subject: Why is ascorbic acid an acid if it has no COOH group?

I have a students who is comparing ascorbic acid and citric acid as pH modifiers 
in an experiment to look at denaturing of the bromelain enzyme in pineapple.  On 
consideration of the structure of ascorbic acid to explain its effect I see it 
has no carboxyl group only hydroxyl groups and a carbonyl group.  Does the 
carbonyl group on an adjacent carbon sufficiently withdraw and delocalise 
electrons to cause the dissociation of the hydroxyl group on the next carbon 
atom to cause the acidity of ascorbic acid?

Re: Why is ascorbic acid an acid if it has no COOH group?