Document Type

Article

Publication Date

2011

Publication Title

Applied General Topology

DOI

10.4995/agt.2011.1648

Abstract

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.

Comments

This journal is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. Article obtained from the Applied General Topology.

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Mathematics Commons

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