S-闭空间中的一些性质

An Analysis of Genesis of Lining Cracks in No.5 Tunnel of Luohui Irrigation Canal

主要研究Ｓ－闭空间的分离性与映射。首先讨论了Ｓ－闭空间的分离性，证明Ｔ＊１型的Ｓ－闭空间与Ｔ２型Ｓ－闭空间是相同的，正则的Ｓ－闭空间与正规的Ｓ－闭空间是相同的，从而得到要使Ｔ＊１型空间Ｘ成为Ｓ－闭空间的充要条件是Ｘ为极不连通的Ｈ－闭空间，Ｓ－闭空间Ｘ可度量化的充要条件是Ｘ为Ｓ－闭的Ｔ１型正则（Ａ１）空间。其次讨论了Ｓ－闭空间的映射，得到的主要结果是：若ｆ是Ｓ－闭空间Ｘ到度量空间Ｙ的连续映射，则ｆ（Ｘ）是有界的；若ｆ是Ｓ－闭空间Ｘ上的实值连续泛函，则ｆ能在Ｘ的点处达到它的最大值与最小值。

The flowing sand and high groundwater table can cause the difficulty to the construction of No.5 tunnel of Luohui Canal, and its structure is also subject to the unfavourable impact so as to make the tunnel lining produce cracks in its construction. This paper analyses the genesis of cracks and advances some suggestions and measures to prevent the cracks from occurence.