Glasnik Matematicki, Vol. 50, No. 2 (2015), 467-488.

MORE ON STRONG SIZE PROPERTIES

Sergio Macías and César Piceno

Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, México D. F., C. P. 04510, México
e-mail: sergiom@matem.unam.mx
e-mail: cesarpicman@hotmail.com


Abstract.   We continue our study of strong size maps. We show that strong size levels for the n-fold hyperspace of a continuum contain (n-1)-cells. We give two constructions of strong size maps. We introduce reversible strong size properties. We prove that each of the following properties: being a continuum chainable continuum, being a locally connected continuum, and being a continuum with the property of Kelley, is a reversible strong size property. Following Professors Goodykoontz and Nadler, we define admissible strong size maps and show that the levels of admissible strong size maps for the n-fold hyperspace of a locally connected continuum are homeomorphic to the Hilbert cube. Professor Benjamín Espinoza defined Whitney preserving maps for the hyperspace of subcontinua of a continuum. We define strong size preserving maps and show that this class of maps coincides with the class of homeomorphisms.

2010 Mathematics Subject Classification.   54B20.

Key words and phrases.   Absolute retract, acyclic continuum, admissible strong size map, continuum, continuum chainable continuum, Hilbert cube, n-fold hyperspace, n-fold symmetric product, retract, retraction, reversible strong size property, strong size level, strong size map, strong size properties.


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DOI: 10.3336/gm.50.2.14


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