Vol. 93, No. 2, 1981

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On the topology of direct limits of ANRs

Richard Elam Heisey and Henryk Torunczyk

Vol. 93 (1981), No. 2, 307–312
Abstract

Let {(Xn,an)} be a sequence of pointed, locally compact, finite-dimensional, nondegenerate, connected ANR’s. It is shown that the direct limit of the system

X1 X1 ×{a2}⊂ X1 × X2 X1 × X2 ×{a3}⊂ X1 × X2 × X3
is homeomorphic to an open subset of R = li→mRn, R the reals. As a consequence, if f : X Y is a homotopy equivalence between ANR’s as above then lim
→fn : lim
→Xn lim
→Y n is homotopic to a homeomorphism.

Mathematical Subject Classification 2000
Primary: 57N20
Secondary: 54C55, 58B20
Milestones
Received: 15 June 1979
Revised: 7 February 1980
Published: 1 April 1981
Authors
Richard Elam Heisey
Henryk Torunczyk