The span for Hausdorff continua

Peláez, Antonio

doi:10.1090/S0002-9939-09-10123-5

The span for Hausdorff continua
HTML articles powered by AMS MathViewer

by Antonio Peláez PDF

Proc. Amer. Math. Soc. 138 (2010), 1113-1120 Request permission

Abstract:

The author previously defined the surjective semispan for Hausdorff continua and he proved that chainable continua have empty surjective semispan. In this paper, we define the semispan, the surjective span and the span of a Hausdorff continuum. We characterize the emptiness of these notions in terms of universal mappings to prove that a continuum has empty span (semispan) if and only if each of its subcontinua has empty surjective span (semispan). We also prove that the emptiness of these notions is invariant under inverse limits.

References

Ryszard Engelking, General topology, 2nd ed., Sigma Series in Pure Mathematics, vol. 6, Heldermann Verlag, Berlin, 1989. Translated from the Polish by the author. MR 1039321
K. P. Hart and B. J. van der Steeg, Span, chainability and the continua $\Bbb H^*$ and $\Bbb I_u$, Topology Appl. 151 (2005), no. 1-3, 226–237. MR 2139754, DOI 10.1016/j.topol.2004.03.007
A. Lelek, Disjoint mappings and the span of spaces, Fund. Math. 55 (1964), 199–214. MR 179766, DOI 10.4064/fm-55-3-199-214
A. Lelek, On the surjective span and semispan of connected metric spaces, Colloq. Math. 37 (1977), no. 1, 35–45. MR 482680, DOI 10.4064/cm-37-1-35-45
A. Peláez, The surjective semispan for Hausdorff continua, to appear in Topology and its Applications.