WordNet sense 1 (a very small distance or space):

hairsbreadth, whisker, hair's-breadth

WordNet sense 2 (filamentous hairlike growth on a plant):

fuzz, tomentum

WordNet sense 3 (any of the cylindrical filaments characteristically growing from the epidermis of a mammal):

pilus

WordNet sense 4 (cloth woven from horsehair or camelhair; used for upholstery or stiffening in garments):

haircloth