Geodesic
Approximative and fundamental retracts
Sbornik. Mathematics, Tome 22 (1974) no. 1, pp. 91-103 Cet article a éte moissonné depuis la source Math-Net.Ru

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A positive answer is given to the following question of Borsuk: is a movable space $X_0$ which is a connected component of a compactum $X$ a fundamental retract of the latter? There is then defined and studied the notion of an internally movable space, which has many of the properties of a movable space in the sense of Borsuk. In addition, an examination is made of the interrelations between the various classes of absolute (neighborhood) retracts. For example, it is proved that the absolutely approximative retracts are precisely those fundamental absolute retracts that are simultaneously absolute approximative neighborhood retracts in the sense of Clapp (or of Noguchi). Bibliography: 8 titles. 
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S. A. Bogatyi. Approximative and fundamental retracts. Sbornik. Mathematics, Tome 22 (1974) no. 1, pp. 91-103. http://geodesic.mathdoc.fr/item/SM_1974_22_1_a5/

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[2] K. Borsuk, “Fundamental retracts and extensions of fundamental sequences”, Fundam. math., 64:1 (1969), 55–85 | MR | Zbl

[3] Michael H. Clapp, “On a generalization of absolute neighborhood retracts”, Fundam. math., 70 (1971), 117–130 | MR | Zbl

[4] D. M. Hyman, “ANR divisors and absolute neighborhood contractibility”, Fundam. math., 62:1 (1968), 61–73 | MR | Zbl

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[6] K. Borsuk, Theory of shape, Lecture Notes Series, 28, AARHUS universitet, 1971 | MR | Zbl

[7] A. Gmurczyk, “Approximative retracts and fundamental retracts”, Colloq. Máth., 23:1 (1971), 61–63 | MR | Zbl

[8] J. Dugundji, “An extension of Tietze's theorem”, Pacific J. Math., 1 (1951), 353–367 | MR | Zbl