  This work provides a generalization of the Gelfand duality to the context of
noncommutative locally $C^*$ algebras. Using a reformulation of a theorem
proven by Dauns and Hofmann in the 60's we show that every locally $C^*$
algebra can be realized as the algebra of continuous sections of a $C^*$ bundle
over a compactly generated topological space. This result is used then to show
that on certain special cases locally $C^*$ algebras can be used to define
certain sheaves of locally $C^*$ algebras that, inspired by the analogy with
commutative geometry, we call noncommutative spaces. The last section provides
some examples, motivated by mathematical physics, for this definition of
noncommutative space. Namely we show that every local net of $C^*$ algebras
defines a noncommutative space and, based on a loose generalization of the
original construction by Doplicher, Fredenhagen and Roberts, construct what we
propose to call a "locally covariant quantum spacetime".
