A+ CATEGORY SCIENTIFIC UNIT

$n$-Arc connected spaces

Volume 130 / 2013

Benjamin Espinoza, Paul Gartside, Ana Mamatelashvili Colloquium Mathematicum 130 (2013), 221-240 MSC: Primary 54F15; Secondary 54D05, 54F15, 54H05. DOI: 10.4064/cm130-2-5

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 $\aleph _0$-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.

Authors

  • Benjamin EspinozaDepartment of Mathematics
    University of Pittsburgh at Greensburg
    236 Frank A. Cassell Hall
    150 Finoli Drive
    Greensburg, PA 15601, U.S.A.
    e-mail
  • Paul GartsideDepartment of Mathematics
    University of Pittsburgh
    508 Thackeray Hall
    Pittsburgh, PA 15260, U.S.A.
    e-mail
  • Ana MamatelashviliDepartment of Mathematics
    University of Pittsburgh
    301 Thackeray Hall
    Pittsburgh, PA 15260, U.S.A.
    e-mail

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