In the second part of this article, we show that if Z is a metacompact subspace of a GO-space X and $\mathcal{U}$ is a family of open subsets of X such that $Z\subset \bigcup \mathcal{U}$ then there exists a point-finite family $\mathcal{V}$ of open subsets of X such that $Z\subset \bigcup \mathcal{V}$ and $\mathcal{V}\prec \mathcal{U}$. Thus every subspace Y of a GO-space X is metacompact in X if and only if Y is a metacompact subspace of X.

In the third part of this article, we get the following conclusions. We show that if $(X,\tau ,<)$ is a GO-space and Z is a monotonically (countably) metacompact subspace of X, then Z is monotonically (countably) metacompact in X. By this conclusion we show that if $(X,\tau ,<)$ is a GO-space with property $(\mathrm{B})$ such that the maximal dense in itself set Z of X is a monotonically (countably) metacompact subspace of X, then X is monotonically (countably) metacompact. This gives a partial answer to [8, Question].

In the fourth part of this article, we show that if X is in PIGO and X is a countable unions of D-spaces, then X is a D-space, where PIGO is the class of perfect images of GO-spaces.

In the last part of this article we point out that there is an error in the proof of Theorem 10 in (2018) [23]. Then we finally give a new proof for it.

在本文的第二部分中，我们证明了Z是GO空间X的超紧凑子空间，并且$\mathcal{ü}$是X的开放子集的族，使得$ž\subset \bigcup \mathcal{ü}$ 然后有一个点有限的家庭 $\mathcal{伏特}$打开子集的X，使得$ž\subset \bigcup \mathcal{伏特}$ 和 $\mathcal{伏特}\prec \mathcal{ü}$。因此，当且仅当Y是X的超紧致子空间时，GO空间X的每个子空间Y才是X中的超紧致。

在本文的第三部分，我们得出以下结论。我们证明，如果$（X，\tau ，<）$是一个GO-空间和ž是单调（可数）亚紧的子空间X，然后ž是单调（可数）亚紧X。根据这一结论，我们表明，如果$（X，\tau ，<）$ 是一个具有属性的GO空间 $（\mathrm{乙}）$使得在自身的最大密设置ž的X是单调（可数）亚紧的子空间X，那么X是单调（可数）亚紧。这给出了对[8，问题]的部分回答。

在这篇文章中的第四部分，我们证明，如果X是PIGO和X是可数工会d -spaces，那么X是d k空间，其中PIGO是类GO-空间的完美图像。

在本文的最后部分，我们指出（2018）[23]中的定理10的证明存在错误。然后，我们终于为其提供了新的证明。