Lectures on Hilbert Cube Manifolds

A Fake Topological Hilbert Space

“…We will show that the space Y = ß \ UJ° W/ has the properties specified in §1, except for the negligibility property (6). It then follows that, for any countable dense set D G Y, the space X= Y\D has all the required properties (Theorem 5.3).…”

“…We first construct a tower Ax G A2G ... of compact AR's in ß satisfying the conditions (4) and (5), and then take Bn -AnX QX I" X {(1,1,...)} C ß X ß X ß. By Edward's product theorem (see [6] …”

Canonical covers and dimension of Z-sets in the Hilbert cube

“…For the reader's convenience we recommend [3] for the study of Z-sets; see also [6,8] for dimension theory and [10] for a global view of coarse geometry concepts quoted, but not used, in this paper.…”

Concerning exactly (𝑛,1) images of continua

“…It follows that / is an exactly (n, l) mapping, and hence/X l: X X Q -Y X Q is exactly (n,\) where l denotes the identity map on Q. By combining 44.1 and 22.1 of [2], it follows that A X Q is a Hubert cube. Clearly, Y X Q is a Hubert cube.…”