Topologies on Pseudo-Trees and Applications

ยท American Mathematical Soc.
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116
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A pseudo-tree is a partially ordered set such that the set of all predecessors of any element is linearly ordered. Clearly, each linearly ordered set is a pseudo-tree and pseudo-trees are, in general, much more complicated objects than chains. The aim of this paper is to develop a theory of natural order topologies on pseudo-trees which extends the theories of linearly ordered topological spaces and GO-spaces. Moreover, applications are given for some classes of continua which admit a natural ordering.

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