Its somewhat annoying to prove some space has a CW complex structure; I'm not really motivated to do it.
The following spaces are CW complexes which do not yet have the trait: S25,S139,S158,S168,S176,S198,S210,S225.
All other space for which the trait is unknown are not CW complexes by theorem in #1769. Only exception is S179 for which it is consisten with ZFC its not a CW compact (and realistically also provably not, but we dont know a lot about the space).
Its somewhat annoying to prove some space has a CW complex structure; I'm not really motivated to do it.
The following spaces are CW complexes which do not yet have the trait: S25,S139,S158,S168,S176,S198,S210,S225.
All other space for which the trait is unknown are not CW complexes by theorem in #1769. Only exception is S179 for which it is consisten with ZFC its not a CW compact (and realistically also provably not, but we dont know a lot about the space).