View source for Approximately-compact set

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A set having the property of [[Approximate compactness|approximate compactness]]. A metric projection on any approximately-compact Chebyshev set is continuous. Examples of approximately-compact sets include boundedly-compact sets and closed convex sets in the spaces $L_p$ ($0<p<\infty$), and the set of rational fractions in which the degrees of the numerator and denominator are constant. In approximation theory and in the theory of ill-posed problems frequent use is made of spaces in which all closed sets are approximately compact.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  N.V. Efimov,   S.B. Stechkin,   "Approximative compactness and Čebyšev sets"  ''Soviet Math. Dokl.'' , '''2''' :  5  (1961)  pp. 1226–1228  ''Dokl. Akad. Nauk SSSR'' , '''140''' :  3  (1961)  pp. 522–524</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  L.P. Vlasov,   "Approximative properties of sets in normed linear spaces"  ''Russian Math. Surveys'' , '''28''' :  6  (1973)  pp. 1–66  ''Uspekhi Mat. Nauk'' , '''28''' :  6  (1973)  pp. 3–66</TD></TR></table>