Approximative and fundamental retracts

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.