n-Arc Connected Spaces release_avguosl6bbflnj3e7z4xk4cue4

by Benjamin Espinoza, Paul Gartside, Ana Mamatelashvili

Released as a article .

2012  

Abstract

A space is `n-arc connected' (n-ac) if any family of no more than n-points are contained in an arc. For graphs the following are equivalent: (i) 7-ac, (ii) n-ac for all n, (iii) continuous injective image of a closed sub-interval of the real line, and (iv) one of a finite family of graphs. General continua that are aleph_0-ac are characterized. The complexity of characterizing n-ac graphs for n=2,3,4,5 is determined to be strictly higher than that of the stated characterization of 7-ac graphs.
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Date   2012-09-24
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arXiv  1209.5451v1
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