Research Article

Smallness in topology

Published in: Quaestiones Mathematicae
Volume 46 , issue S1 : SPECIAL ISSUE DEDICATED TO THE MEMORY OF PROFESSOR HORST HERRLICH , 2023 , pages: 13–39

DOI: 10.2989/16073606.2023.2247720

Author(s): Jiří Adámek Czech Technical University, Czech Republic , Miroslav Hušek Charles University, Czech Republic , Jiří Rosický Masaryk University, Czech Republic , Walter Tholen York University, Canada

Keywords: 18F60 , 54B30 , 54D10 , Finitely presentable object , finitely generated object , finitely small object , directed colimit , Hausdorff space , T₀-space , T₁-space , compact space

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Abstract

Quillen’s notion of small object and the Gabriel-Ulmer notion of finitely presentable or generated object are fundamental in homotopy theory and categorical algebra. Do these notions always lead to rather uninteresting classes of objects in categories of topological spaces, such as all finite discrete spaces, or just the empty space, as the examples and remarks in the existing literature may suggest?

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