Universal elements for some classes of spaces


  • D. N. Georgiou University of Patras
  • Stavros Iliadis University of Patras
  • A. C. Megaritis University of Patras




Dimension-like function, Saturated class, Universal space


In the paper two dimensions, denoted by dm and Dm, are defined in the class of all Hausdorff spaces. The dimension Dm does not have the universality property in the class of separable metrizable spaces because the family of all such spaces X with Dm(X) < 0 coincides with the family of all totally disconnected spaces in which there are no universal elements. In we gave the dimension-like functions dmK,B E and DmK,B E, where K is a class of subsets, E a class of spaces and B a class of bases and we proved that in the families P(dm K, B E < K)and P(Dm K, B E < K) of all spaces X for which dm K,B E (X) < K and Dm K, B E (X) < K, respectively there exist universal elements. In this paper, we give some new dimension-like functions and define using these definitions classes of spaces in which there are universal elements.


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Author Biographies

D. N. Georgiou, University of Patras

Department of Mathematics

Stavros Iliadis, University of Patras

Department of Mathematics

A. C. Megaritis, University of Patras

Department of Mathematics


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S. D. Iliadis, Universal spaces and mappings, North-Holland Mathematics Studies, 198. Elsevier Science B.V., Amsterdam, 2005. xvi+559 pp.

D. N. Georgiou, S. D. Iliadis and A.C. Megaritis, Dimension-like functions and universality, Topology Appl. 155 (2008), 2196-2201. https://doi.org/10.1016/j.topol.2007.05.024

A. K. O'Connor, A new approach to dimension, Acta Math. Hung. 55, no. 1-2 (1990), 83-95. https://doi.org/10.1007/BF01951390

R. Pol, There is no universal totally disconnected space, Fund. Math. 79 (1973), 265-267. https://doi.org/10.4064/fm-79-3-265-267


How to Cite

D. N. Georgiou, S. Iliadis, and A. C. Megaritis, “Universal elements for some classes of spaces”, Appl. Gen. Topol., vol. 12, no. 2, pp. 193–211, Oct. 2011.