Trimming and Building Freezing Sets

We develop new tools for the construction of fixed point sets in digital topology. We define excludable points and show that these may be excluded from all freezing sets. We show that articulation points are excludable. We also present results concerning points that must belong to a freezing set and often are easily recognized. These include points of degree~1 and some local extrema.
Comment: This submission replaces a withdrawn paper. It contains material quoted or paraphrased from earlier papers; sources are noted. arXiv admin note: text overlap with arXiv:2304.07365