A note on the rank of diagonals

摘要

For each natural number k ≥ 4, we construct a Tychonoff space with a rank k-diagonal but without a rank (k + 1)-diagonal. This example proves a conjecture on rank of diagonal given by A.V. Arhangel'skii and R.Z. Buzyakova (2006) in [1] and answers some questions raised by them in the same paper.