  This article deals with a continuous closed 1-form defined on a CW-complex.
In particular, we show Lusternik-Schnirelmann type theory on continuous closed
1-forms which is related to gradient-like flows. M.Farber defined a continuous
closed 1-form and a category with a respect to a cohomology class and
constructed a Lusternik-Schnirelman Theory for smooth closed 1-forms. We denote
about a definition of a zero-point of continuous closed 1-form and generalize
this theory to continuous closed 1-forms. It shows a relation between the
number of a zero-point of continous closed 1-form and the category with a
respect to a cohomology class, through a dynamical system on a original space,
homoclinic cycle.
