Glasnik Matematicki, Vol. 53, No. 2 (2018), 359-370.

Rⁱ-SETS, PSEUDO-CONTRACTIBILITY AND WEAK CONTRACTIBILITY ON HYPERSPACES OF CONTINUA

Félix Capulín, Leonardo Juárez-Villa and Fernando Orozco-Zitli

Facultad de Ciencias,, Instituto Literario No. 100, Col. Centro, C. P. 50000,, Toluca, Estado de México, México
e-mail: fcapulin@gmail.com
e-mail: juvile06@gmail.com, ljuarezv@uaemex.mx
e-mail: forozcozitli@gmail.com

Abstract.   In this paper we discuss the notions of pseudo-contractibility and weak contractibility on hyperspaces of (Hausdorff) continua. Also we prove that if a continuum X contains an Rⁱ-set then it is not pseudo-contractible. As a consequence we have that the existence of an Rⁱ-set in a continuum X implies non(pseudo)-contractibility of some hyperspaces.

2010 Mathematics Subject Classification.   54C05, 54C10, 54B20, 54B15

Key words and phrases.   Continuum, hyperspace, contractibilty

DOI: 10.3336/gm.53.2.08

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