On spaces which are essentially T1

摘要

Let S be a pseudo-metric space with pseudo-metric d. Then for each nonempty A a?? S, x a?? cl (A) if and only if d(x, A) = 0, and d(x, y) = d(y, x) for all x, y a??S. Thus, if d(x, y) = 0, then xa??cl({Y}) by the first requirement and Ya??cl({x}) by the second requirement. It is natural then to expect that if a topological space S is to be pseudo-metrizable, it should at least satisfy the requirement: