End compactifications in non-locally-finite graphs
2001 ◽
Vol 131
(3)
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pp. 427-443
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Keyword(s):
There are different definitions of ends in non-locally-finite graphs which are all equivalent in the locally finite case. We prove the compactness of the end-topology that is based on the principle of removing finite sets of vertices and give a proof of the compactness of the end-topology that is constructed by the principle of removing finite sets of edges. For the latter case there exists already a proof in [1], which only works on graphs with countably infinite vertex sets and in contrast to which we do not use the Theorem of Tychonoff. We also construct a new topology of ends that arises from the principle of removing sets of vertices with finite diameter and give applications that underline the advantages of this new definition.
Keyword(s):
2006 ◽
Vol 96
(2)
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pp. 302-312
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2008 ◽
Vol 22
(4)
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pp. 1381-1392
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1983 ◽
Vol 34
(1)
◽
pp. 48-57
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1971 ◽
Vol 69
(3)
◽
pp. 401-407
◽
1993 ◽
Vol 59
(1)
◽
pp. 15-25
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