Abstract.It is shown that every locally contractible metric space that is the countable union of finite dimensional compacta is an absolute neighborhood retract.
Let Af" be a compact PL manifold, n # 4; if n = 5, suppose 3M is empty. Let H(M) be the space of homeomorphisms on M and H* (M) the elements of H(M) which are isotopic to PL homeomorphisms. It is shown that the space of PL homeomorphisms, PLH(M), has the finite dimensional compact absorption property in H*(M) and hence that (H*(M),PLH(M)) is an (/2,//)-manifold pair if and only if H(M) is an l2manifold. In particular, if M* is a 2-manifold, (H(M2),PLH(M2)) is an (/2,//)-manifold pair. PLHiM) X //is an //-manifold. Finally, Keesling and Wilson [16] have shown that PLHiM) X l{ is homeomorphic to PLHiM). Hence PLHiM) is an l{manifold. In general it is not true that PLHiM) is dense in HiM). For example, Kirby and Siebenmann (see [17]) have shown that HiS2 X S3) has a component containing no PL homeomorphism. They have also shown that if the
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