Displaying 1521 – 1540 of 1977

Showing per page

Some examples related to colorings

Michael van Hartskamp, Jan van Mill (2000)

Commentationes Mathematicae Universitatis Carolinae

We complement the literature by proving that for a fixed-point free map f : X X the statements (1) f admits a finite functionally closed cover 𝒜 with f [ A ] A = for all A 𝒜 (i.e., a coloring) and (2) β f is fixed-point free are equivalent. When functionally closed is weakened to closed, we show that normality is sufficient to prove equivalence, and give an example to show it cannot be omitted. We also show that a theorem due to van Mill is sharp: for every n 2 we construct a strongly zero-dimensional Tychonov space...

Currently displaying 1521 – 1540 of 1977