In this paper we further investigate the results given in [8,9 and 10]. In section 2 we consider locally HCC(SCC,CC) spaces. A topological space $X$ is called locally HCC(SCC,CC) space if for every $x\in X$ there exists a neighbourhood $U$ of the point $x$ such that the closure of $U$ in $X$ is a HCC(SCC,CC) subspace of $X$. In section 3 we consider a one point-extension of a space $X$ related to the property $\mathcal P$, where $\mathcal P$ is one of the properties: compactness, countablle compactness, strong countable compactness, hypercountable compactnes or Lindelöfness. If $(X,\tau)$ is a Hausdorff locally $\mathcal P$ space, then there exists a one-point extension $(\omega X,\omega)$ which is a Hausdorff space and has the property $\mathcal P$. In section 4 we consider some relations between HCC and SCC properties.