Core compactness and diagonality in spaces of open sets


  • Francisco Jordan Queensborough Community College
  • Frédéric Mynard Georgia Southern University



Scott convergence, Scott topology, Upper Kuratowski convergence, Upper Kuratowski topology, Core compact, Diagonal convergence, Pretopology, Consonance, Infraconsonance


We investigate when the space OX of open subsets of a topological space X endowed with the Scott topology is core compact. Such conditions turn out to be related to infraconsonance of X, which in turn is characterized in terms of coincidence of the Scott topology of OX × OX with the product of the Scott topologies of OX at (X,X). On the other hand, we characterize diagonality of OX endowed with the Scott convergence and show that this space can be diagonal without being pretopological. New examples are provided to clarify the relationship between pretopologicity, topologicity and diagonality of this important convergence space.


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Author Biographies

Francisco Jordan, Queensborough Community College

Queensborough Community College, Queens, NY, USA

Frédéric Mynard, Georgia Southern University

Georgia Southern University, Statesboro, GA30460, USA


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How to Cite

F. Jordan and F. Mynard, “Core compactness and diagonality in spaces of open sets”, Appl. Gen. Topol., vol. 12, no. 2, pp. 143–162, Oct. 2011.



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