  A number of authors have reported filaments connecting bright structures in
high-resolution X-ray images, and in some cases these have been taken as
evidence for a physical connection between the structures, which might be
thought to provide support for a model with non-cosmological redshifts. In this
paper I point out two problems which are inherent in the interpretation of
smoothed photon-limited data of this kind, and develop some simple techniques
for the assessment of the reality of X-ray filaments, which can be applied to
either simply smoothed or adaptively smoothed data. To illustrate the
usefulness of these techniques, I apply them to archival ROSAT observations of
galaxies and quasars previously analysed by others. I show that several
reported filamentary structures connecting X-ray sources are not in fact
significantly detected.
