Geodesic
$n$-Arc connected spaces
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.
Colloquium Mathematicum, Tome 130 (2013) no. 2, pp. 221-240 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm130-2-5
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

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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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

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