Core compactness and diagonality in spaces of open sets

Details Core compactness and diagonality in spaces of open sets Core compactness and diagonality in spaces of open sets

2010-11-16

arxiv.org/abs/1011.3574v2

Mathematics

General Topology

revised version 12/06/10: example of a $T$-core compact convergence space that is not $T$-dual added

Scientific paper

We investigate when the space $\mathcal O_X$ 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 $\mathcal O_X\times\mathcal O_X$ with the product of the Scott topologies of $\mathcal O_X$ at $(X,X)$. On the other hand, we characterize diagonality of $\mathcal O_X$ 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.

Affiliated with

Also associated with

No associations

Rating

Core compactness and diagonality in spaces of open sets does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Core compactness and diagonality in spaces of open sets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Core compactness and diagonality in spaces of open sets will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-463487