Theory of Retracts
Robinson, Lawrence Olin (Larry)
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The paper is divided essentially into three parts. In the first, preliminary definitions are given, and the extension problem is defined. We see that from the extension problem, we encounter the retraction problem. The retraction problem provides us with the concepts of retracts and retraction maps. At the end of the first part, we find a proposition which relates more closely the extension and retraction problems. The second part deals with the properties of retracts and their relation to several concepts of topology. Here we will examine such areas as closedness, the fixed-point property, and contractibility from the standpoint of how retracts effect these concepts. The final section examines briefly the theory of absolute extensors and absolute neighborhood extensors. We then inspect a few propositions concerning the relation between retracts, absolute extensors, and absolute neighborhood extensors.