Geodesic
Absolute Approximate Retracts and AR-Spaces
Canadian journal of mathematics, Tome 33 (1981) no. 2, pp. 297-301

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A subset A of a topological space X is an approximateretract of X if for every neighborhood U of A in X there is a retract R of X such that A ⊂ R ⊂ U. A compactum X is an absolute approximate retract (AAR-space) if whenever X is embedded as a subset of a compactum Z, then X is an approximate retract of Z. These concepts were first defined in [2] where it is shown that every AAR-space is a contractible Peano continuum. In [3] an example is given to show that there exists a contractible LC∞ compactum which is not an AAR-space. 
Martin, John R. Absolute Approximate Retracts and AR-Spaces. Canadian journal of mathematics, Tome 33 (1981) no. 2, pp. 297-301. doi: 10.4153/CJM-1981-024-1
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[1] 1. Borsuk, K., Theory of retracts, Monografie Matema t y cz ne 44 (Warszawa, 1967). Google Scholar

[2] 2. Martin, J. R., A generalization of absolute retracts, Proc. Amer. Math. Soc. 52 (1975), 409–413. Google Scholar

[3] 3. Martin, J. R., An example of a contractible LC°° compactant which is not an absolute approximate retract, Bull. Ac. Pol. Sri. 25 (1977), 489–492. Google Scholar

[4] 4. Martin, J. R., Absolute fixed point sets and AR-spaces, Fund. Math, (to appear). Google Scholar

[5] 5. Martin, J. R., Absolute fixed point sets in compacta, Colloq. Math. 39 (1978), 41–44. Google Scholar

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