 Reflective Relatives of AdjunctionsG. Richter
A chapter in Categorical Topology, 1996, pp 31-41 from Springer Abstract: Abstract Every map T → UX from a set T to the underlying set UX of a compact Hausdorff space X admits a unique continuous extension βT → X from the Čech-Stone-compactification βT of T to X. Is it true for an arbitrary space X with this unique extension property to be already compact Hausdorff? No, there is a sophisticated counterexample [8]. Consequently, it makes sense to investigate the full subcategory of all such spaces in Top, say Comp β, which turns out to be reflective, containing compact Hausdorff spaces as reflective and bicoreflective subcategory. This paper deals with a new topological description of the spaces in Comp β, which yields more natural examples up to a finally dense class. Moreover, it turns out that there are very abstract categorical reasons for the concrete topological observations above. Keywords: Čech-Stone-compactification; continuous images of compact Hausdorff spaces; convergence structures; (almost) reflective and coreflective subcategories; factorization-systems for morphisms and sources; topological functors; 54B30; 18B30; 18A40; 54A20; 54D30; 54D35 (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-0263-3_3 Ordering information: This item can be ordered from DOI: 10.1007/978-94-009-0263-3_3 Access Statistics for this chapter More chapters in Springer Books from Springer |
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