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The paper deals with counting sets of given magnitude whose elements are self-avoiding paths with nodes from a fixed set of points on a circle. Some of the obtained formulae provide new properties of entries in ``The On-line Encyclopaedia of Integer Sequences", while others generate new entries therein.
We prove several stability properties for the class of compact Hausdorff spaces such that with the weak or the pointwise topology is in the class of Stegall. In particular, this class is closed under arbitrary products.
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