the homotopy type of the pointed loop space of a countable cw complex

Question

I apologize in advance if this is too elementary for this forum. I have received some help but am still unsure about how to proceed. I am interested in a proof of the following result due to John Milnor: If X is a countable CW complex then the pointed loop space of X (with the compact open topology) has the homotopy type of a CW complex. I have consulted Milnor's "on spaces having the homotopy type of a CW complex" but it references articles I was unable to find after determined searches on google scholar. Does anyone know of a self-contained exposition of this result?

Answer 1

There is a very fine book ``Cellular structures in topology'', by R. Fritsch and R.A. Piccinini that gives a detailed and self-contained treatment of Milnor's results. It has a wealth of other well-presented material, some of which is little known nowadays.