Graffiti it is a rapidly developing art form whose value is highly contested and reviled by many authorities while also subject to protection, sometimes within the same jurisdiction. Both "graffiti" and its occasional singular form "graffito" are from the Italian word "graffiato" ("scratched"). "Graffiti" is applied in art history to works of art produced by scratching a design into a surface. A related term is "sgraffito", which involves scratching through one layer of pigment to reveal another beneath it. This technique was primarily used by potters who would glaze their wares and then scratch a design into it. In ancient times
Singular homology on singular "n"-chains. The extension, called the boundary operator, written as is a homomorphism of groups. The boundary operator, together with the formula_25, form a chain complex of abelian groups, called the singular complex. It is often denoted as formula_26 or more simply formula_27. The kernel of the boundary operator is formula_28, and is called the group of singular "n"-cycles. The image of the boundary operator is formula_29, and is called the group of singular "n"-boundaries. It can also be shown that formula_30. The formula_31-th homology group of formula_32 is then defined as the factor group The elements of formula_34