  In this article we study a homotopy invariant cat(X,B,\xi) on a pair of
finite CW complexes with respect to a continuous closed 1-form. This is a
generalisation of a Lusternik-Schnirelmann category developed by Farber,
studying the topology of a closed 1-form. The article establishes the
connection with the original notion and obtains analogous results on critical
points and homoclinic cycles. We also provide a similar cuplength lower bound
for cat(X,B,\xi).
