A hit-and-miss topology for $2^X$, $C_{n}(X)$ and $F_{n}(X)$

Volume 115 / 2009

Benjamín Espinoza, Verónica Martínez-de-la-Vega, Jorge M. Martínez-Montejano Colloquium Mathematicum 115 (2009), 47-64 MSC: Primary 54B20; Secondary 54F15, 54A10. DOI: 10.4064/cm115-1-6

Abstract

A hit-and-miss topology ($\tau_{\rm HM}$) is defined for the hyperspaces $2^X$, $% C_n(X)$ and $F_n(X)$ of a continuum $X$. We study the relationship between $% \tau_{\rm HM}$ and the Vietoris topology and we find conditions on $X$ for which these topologies are equivalent.

Authors

  • Benjamín EspinozaDepartment of Mathematics
    University of Pittsburgh at Greensburg
    1150 Mt. Pleasant Rd.
    Greensburg, PA 15601, U.S.A.
    e-mail
  • Verónica Martínez-de-la-VegaInstituto de Matemáticas
    Universidad Nacional Autónoma de México
    Área de la investigación científica
    Circuito exterior
    Ciudad Universitaria
    México, D.F., 04510,
    México
    e-mail
  • Jorge M. Martínez-MontejanoInstituto de Matemáticas
    Universidad Nacional Autónoma de México
    Área de la investigación científica
    Circuito exterior
    Ciudad Universitaria
    México, D.F., 04510,
    México
    e-mail

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