On p. 221 of http://topology.auburn.edu/tp/reprints/v08/tp08113.pdf, I found the following definition:
"A curve is said to be cyclic if its first Čech cohomology group with integer coefficients does not vanish".
Here, a curve means a homogeneous metric continuum of dimension 1.
Can someone explain this definition in different, more elementary, terms, and give some examples to illustrate the meaning?