Vol. 30, No. 3, 1969

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
Cell-like mappings. I

R. C. Lacher

Vol. 30 (1969), No. 3, 717–731

Cell-like mappings are introduced and studied. A space is cell-like if it is homeomorphic to a cellular subset of some manifold. A mapping is cell-like if its point-inverses are celllike spaces. It is shown that proper, cell-like mappings of ENR’S (Euclidean NR’s) form a category which includes both proper, contractible maps of ENR’s and proper, cellular maps from manifolds to ENR’s. It is difficult to break out of the category: The image of a proper, cell-like map on an ENR, is again an ENR, provided the image is finite-dimensional and Hausdorff.

Some applications to (unbounded) manifolds are given. For example: A cell-like map between topological manifolds of dimension 5 is cellular. The property of being an open n-cell, n 5, is preserved under proper, cell-like maps between topological manifolds. The image of a proper, cellular map on an n-manifold is a homotopy n-manifold.

Mathematical Subject Classification
Primary: 55.25
Secondary: 54.00
Received: 26 June 1968
Published: 1 September 1969
R. C. Lacher