Abstract
It is well known that every epireflective, full subcategory of the category Comp 2 of compact Hausdorff spaces is algebraic in the sense of HERRLICH [6,§32]. Conversely, every algebraic, epireflective, full subcategory of the category of all Hausdorff spaces is contained in Comp 2. This generalizes a result of HERRLICH and STRECKER [5] and yields a complete new proof for it. The lattice of such algebraic categories is very large.
For arbitrary full subcategories C of topological (not necessary Hausdorff) spaces the following holds:
If C is algebraic, closed-hereditary, and contains the ordinal spaces [O,β] for every limit ordinal β then each space in C is compact (not necessary Hausdorff).
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© 1982 Springer-Verlag
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Richter, G. (1982). Algebraic categories of topological spaces. In: Kamps, K.H., Pumplün, D., Tholen, W. (eds) Category Theory. Lecture Notes in Mathematics, vol 962. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066907
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DOI: https://doi.org/10.1007/BFb0066907
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