$n$-Arc connected spaces

Benjamin Espinoza; Paul Gartside; Ana Mamatelashvili

doi:10.4064/cm130-2-5

pl / Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

$n$ -Arc connected spaces

Tom 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

Streszczenie

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.

Autorzy

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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Colloquium Mathematicum

n-Arc connected spaces

Tom 130 / 2013

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$n$ -Arc connected spaces