Geodesic
Operations on Approximatively Compact Sets
Matematičeskie zametki, Tome 82 (2007) no. 5, pp. 729-735.

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In the paper, the problem of preserving the property of approximative compactness under diverse operations is considered. In an arbitrary uniformly convex separable space, we construct an example of two approximatively compact sets whose intersection is not approximatively compact. An example of two linear approximatively compact sets for which the closure of their algebraic sum is not approximatively compact is constructed. In an arbitrary Banach space, we construct two nonlinear approximatively compact sets whose algebraic sum is closed but not approximatively compact. We also prove that any uniformly closed Banach space contains an approximatively compact cavity.
Keywords: Approximatively compact set, algebraic sum of sets, uniformly closed Banach space, Efimov–Stechkin space. 
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I. A. Pyatyshev. Operations on Approximatively Compact Sets. Matematičeskie zametki, Tome 82 (2007) no. 5, pp. 729-735. http://geodesic.mathdoc.fr/item/MZM_2007_82_5_a7/

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