Introduced by C. C. Chang in the late fifties as the Lindenbaum algebras of the infinite-valued calculus of Lukasiewicz, MV-algebras have been attracting renewed interest in the last decade, because they form an equational class being naturally equivalent to the category of lattice-ordered abelian groups with strong unit. As a consequence, countable MV-algebras are in one-one correspondence with AF \(C^*\)-algebras whose Murray-von Neumann order of projections is a lattice. The prime ideal spectrum \(\text{Spec} (A)\) of any MV-algebra \(A\) is homeomorphic to the structure space of its corresponding AF \(C^*\)-algebra. As a partially ordered set, Spec\((A)\) is a spectral root system, and -- as shown by the authors in a forthcoming paper in the Journal of Algebra -- every spectral root system arises from some MV-algebra. As a special case, in the present paper the authors give several characterizations of the class of hypernormal MV-algebras, those MV-algebras \(A\) for which \(\text{Spec}(A)\) is a cardinal sum of chains. For any topological space \(X\), let \(W(X)\) be the MV-algebra of continuous \([0,1]\)-valued functions defined on \(X\). Then the authors prove that \(X\) is an \(F\)-space iff \(W(X)\) is hypernormal. Other similar results are proved, and a number of examples are presented.