like "normal regular space" and "normal Hausdorff space" also turn up in the literature--they simply mean that the space both is normal and satisfies the other condition mentioned. In particular, a normal Hausdorff space is the same thing as a T₄ space. Given the historical confusion of the meaning of the terms, verbal descriptions when applicable are helpful, that is, "normal Hausdorff" instead of "T₄", or "completely normal Hausdorff" instead of "T₅".