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Pretrees and the shadow topology

Author: A. V. Malyutin
Translated by: the author
Original publication: Algebra i Analiz, tom 26 (2014), nomer 2.
Journal: St. Petersburg Math. J. 26 (2015), 225-271
MSC (2010): Primary 54F50
Published electronically: February 3, 2015
MathSciNet review: 3242036
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Abstract: A further development of the theory of pretrees, started by the work of L. Ward, P. Duchet, B. Bowditch, S. Adeleke and P. Neumann, and others, is presented. In particular, a relationship between this theory and the theory of convex structures is established. The shadow topology is investigated in detail. This remarkable topology emerges on tree-like objects of various types and has broad application.

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Additional Information

A. V. Malyutin
Affiliation: St. Petersburg Branch, Steklov Institute of Mathematics, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia

Keywords: Tree, pretree, pseudotree, dendritic space, dendron, dendrite, R-tree, betweenness, interval space, convexity, variety of convex structures, antimatroid, Krein--Milman theorem, shadow topology, observers' topology, Lawson topology, space of ends, syzygy
Received by editor(s): December 25, 2012
Published electronically: February 3, 2015
Additional Notes: Partially supported by RFBR (grants 11-01-00677-a and 11-01-12092-ofi-m) and the RF President Grant MD-5118.2011.1.
Article copyright: © Copyright 2015 American Mathematical Society