Which spaces have a coarser connected Hausdorff topology?

We present some answers to the title. For example, if K is compact, zero-dimensional and D is discrete, then K⊕D has a coarser connected topology iff w(K)⩽2|D|. Similar theorems hold for ordinal spaces and spaces K⊕D where K is compact, not necessarily zero-dimensional. Every infinite cardinal has a...

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Bibliographic Details
Published in:Topology and its applications 2002-11, Vol.125 (2), p.215-231
Main Authors: Fleissner, William, Porter, Jack, Roitman, Judith
Format: Article
Language:English
Subjects:
Coarser topology
Condense
Connected
Extension
Franklin–Rajagopolan space
Minimal Hausdorff
Ordinal
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Summary:We present some answers to the title. For example, if K is compact, zero-dimensional and D is discrete, then K⊕D has a coarser connected topology iff w(K)⩽2|D|. Similar theorems hold for ordinal spaces and spaces K⊕D where K is compact, not necessarily zero-dimensional. Every infinite cardinal has a coarser connected Hausdorff topology; so do Kunen lines, Ostaszewski spaces, and Ψ-spaces; but spaces X with X⊂βω and |βω⧹X|
ISSN:0166-8641
1879-3207
DOI:10.1016/S0166-8641(01)00274-7