Glasnik Matematicki, Vol. 48, No. 1 (2013), 103-114.

STRONG SIZE PROPERTIES

Sergio Macías and César Piceno

Abstract.   We prove that countable aposyndesis, finite-aposyndesis, continuum chainability, acyclicity (for n≥ 3), and acyclicity for locally connected continua are strong size properties. As a consequence of our results we obtain that arcwise connectedness is a strong size property which is originally proved by Hosokawa.

2010 Mathematics Subject Classification.   54B20.

Key words and phrases.   Absolute retract, acyclic continuum, continuum, continuum chainable continuum, countable aposyndesis, deformation retract, finite aposyndesis, n-fold hyperspace, retract, retraction, strong size level, strong size map, strong size properties.

DOI: 10.3336/gm.48.1.10

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