Abstract: | We establish a necessary and sufficient topological condition for maps that are in W1,p(M, N) to be connected by continuous paths in W1,p(M, N) to maps in W1,q(M, N), q > q ≥ 1. We also obtain a necessary and sufficient topological condition under which W1,q(M, N) is strongly dense in W1,p(M, N). Several results concerning sequential weak density of smooth (or W1,q(M, N) maps in W1,p(M, N) are also proven. © 2003 Wiley Periodicals, Inc. |