In the paper, some properties of functions continuous with respect to a density type strong generalized topology are presented. In particular, it is proved that each real function is approximately continuous with respect to this generalized topology almost everywhere. Moreover, some separation axioms for this generalized topological space are investigated.

中文翻译：

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关于密度类型强广义拓扑连续的函数

在本文中，提出了关于密度型强广义拓扑连续的函数的一些性质。尤其是，事实证明，相对于几乎所有地方的这种广义拓扑，每个实函数都近似连续。此外，研究了该广义拓扑空间的一些分离公理。