Resumen:
The completion theorem for metric spaces is always proven using the space
of Cauchy sequences. In this paper, we give a short and alternative proof of this
theorem via Zorn’s lemma. First, we give a way of adding one point to an incomplete space to get a chosen non-convergent Cauchy sequence convergent. Later,
we show that every metric space has a completion by constructing a partial ordered set of metric spaces. Приводится альтернативное доказательство теоремы о пополнении метрических пространств, основанное на лемме Цорна.
Descripción:
U. Kaya
Bitlis Eren University, Bitlis, Turkey
E-mail: mat-ufuk@hotmail.com. У. Кайя
Университет Битлис Эрен, Битлис, Турция
E-mail: mat-ufuk@hotmail.com