Geodesic
On spaces of nearexistence
Matematičeskie zametki, Tome 60 (1996) no. 2, pp. 278-287

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The notion of subspace of nearexistence is introduced. In particular, it is proved that if $Q$ is a countable compact set, then any subspace $L\subset C(Q)$, $\operatorname{dim}L=\operatorname{codim}L=+\infty$, can be approximated by subspaces of nearexistence. 
@article{MZM_1996_60_2_a8,
     author = {G. M. Ustinov},
     title = {On spaces of nearexistence},
     journal = {Matemati\v{c}eskie zametki},
     pages = {278--287},
     publisher = {mathdoc},
     volume = {60},
     number = {2},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_60_2_a8/}
}
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G. M. Ustinov. On spaces of nearexistence. Matematičeskie zametki, Tome 60 (1996) no. 2, pp. 278-287. http://geodesic.mathdoc.fr/item/MZM_1996_60_2_a8/