n-Arc connected spaces

Benjamin Espinoza, Paul Gartside, and Ana Mamatelashvili. "n-Arc connected spaces." Colloquium Mathematicae 130.2 (2013): 221-240. <http://eudml.org/doc/283639>.

@article{BenjaminEspinoza2013,
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 subinterval of the real line, and (iv) one of a finite family of graphs. General continua that are ℵ₀-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.},
author = {Benjamin Espinoza, Paul Gartside, Ana Mamatelashvili},
journal = {Colloquium Mathematicae},
keywords = {arcwise connected; Borel hierarchy; finite graph; long line; -arc connected},
language = {eng},
number = {2},
pages = {221-240},
title = {n-Arc connected spaces},
url = {http://eudml.org/doc/283639},
volume = {130},
year = {2013},
}

TY - JOUR
AU - Benjamin Espinoza
AU - Paul Gartside
AU - Ana Mamatelashvili
TI - n-Arc connected spaces
JO - Colloquium Mathematicae
PY - 2013
VL - 130
IS - 2
SP - 221
EP - 240
AB - 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 subinterval of the real line, and (iv) one of a finite family of graphs. General continua that are ℵ₀-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.
LA - eng
KW - arcwise connected; Borel hierarchy; finite graph; long line; -arc connected
UR - http://eudml.org/doc/283639
ER -