1Department of Mathematics University of Pittsburgh at Greensburg 236 Frank A. Cassell Hall 150 Finoli Drive Greensburg, PA 15601, U.S.A. 2Department of Mathematics University of Pittsburgh 508 Thackeray Hall Pittsburgh, PA 15260, U.S.A. 3Department of Mathematics University of Pittsburgh 301 Thackeray Hall Pittsburgh, PA 15260, U.S.A.
Colloquium Mathematicum, Tome 130 (2013) no. 2, pp. 221-240
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 $\aleph _0$-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.
Keywords:
space n arc connected n ac family n points contained arc graphs following equivalent ac n ac iii continuous injective image closed subinterval real line finite family graphs general continua aleph ac characterized complexity characterizing n ac graphs determined strictly higher stated characterization ac graphs
Affiliations des auteurs :
Benjamin Espinoza
1
;
Paul Gartside
2
;
Ana Mamatelashvili
3
1
Department of Mathematics University of Pittsburgh at Greensburg 236 Frank A. Cassell Hall 150 Finoli Drive Greensburg, PA 15601, U.S.A.
2
Department of Mathematics University of Pittsburgh 508 Thackeray Hall Pittsburgh, PA 15260, U.S.A.
3
Department of Mathematics University of Pittsburgh 301 Thackeray Hall Pittsburgh, PA 15260, U.S.A.
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title = {$n${-Arc} connected spaces},
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Benjamin Espinoza; Paul Gartside; Ana Mamatelashvili. $n$-Arc connected spaces. Colloquium Mathematicum, Tome 130 (2013) no. 2, pp. 221-240. doi: 10.4064/cm130-2-5
