@MISC{Havlicek98noteson, author = {John Havlicek}, title = {Notes on Wait-Free Spans}, year = {1998} }

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Abstract

simplicial complexes and maps. The topological spaces that arise in the study of fault-tolerant computation in asynchronous distributed systems are given by discrete data, such as configurations of input values for the processes. These spaces can be described using simplicial complexes. In this subsection we give a host of definitions. Abstractly, a simplicial complex is a family K of non-empty finite sets that satisfies the following hereditary property : if X 2 K and X 0 is a non-empty subset of X , then X 0 2 K. A subset L ` K is a subcomplex if L is a simplicial complex, which simply means that L itself satisfies the hereditary property. Given any set K of non-empty finite sets, one may form a simplicial complex K by adding any missing sets required by the hereditary property: K = fX 0 : ; 6= X 0 ` X for some X 2 Kg : The complex K formed in this fashion is said to be generated by the set K. An element X 2 K is called a simplex , and the elements of X are its vertice...