  In this paper, we build up a scaled homology theory, $lc$-homology, for
metric spaces such that every metric space can be visually regarded as "locally
contractible" with this newly-built homology. We check that $lc$-homology
satisfies all Eilenberg-Steenrod axioms except exactness axiom whereas its
corresponding $lc$-cohomology satisfies all axioms for cohomology. This
homology can relax the smooth manifold restrictions on the compact metric space
such that the entropy conjecture will hold for the first $lc$-homology group.
