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Semi-Kelley continua

Volume 163 / 2021

Alejandro Illanes Colloquium Mathematicum 163 (2021), 53-69 MSC: Primary 54F15; Secondary 54B20, 54F50. DOI: 10.4064/cm8053-11-2019 Published online: 1 June 2020


We present an alternative definition to the property of being a semi-Kelley continuum. Using it we are able to extend some results in the literature and to obtain new ones. We give a family of mappings preserving the property of being a semi-Kelley continuum; this family includes retractions, monotone mappings and open mappings. We prove that semi-Kelley continua do not contain $R^{3}$-continua. We show that for fans, being semi-Kelley implies semi-smoothness. We also prove that for a continuum $X$ the following are equivalent: (i) $X\times [0,1]$ is semi-Kelley, (ii) ${\rm cone}(X)$ is semi-Kelley, and (iii) ${\rm suspension}(X)$ is semi-Kelley.


  • Alejandro IllanesInstituto de Matemáticas
    Universidad Nacional Autónoma de México
    Circuito Exterior, Ciudad Universitaria
    Ciudad de México, 04510, México

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