具有Pytkeev^(*)网的空间的映射性质

The mapping properties of the space with certain Pytkeev^(*)networks

讨论具有特定Pytkeev^(*)网的空间的映射性质,证明闭映射和有限到一伪开映射保持具有Pytkeev^(*)网的空间,并更进一步地说明了闭映射保持具有点可数Pytkeev^(*)网的空间.同时,给出例子说明某些具有特定Pytkeev^(*)网的空间不能被一些映射保持.

The paper discusses the mapping properties of the spaces with certain Pytkeev^(*)network are discussed,proves that closed mapping and finite to one pseudo-open mapping preserve Pytkeev^(*)networks,and further demonstrates that closed mapping preserves spaces with point-countable Pytkeev^(*)networks.Meanwhile,some examples are given to illustrate that some spaces with certain Pytkeev^(*)networks cannot be preserved by some mappings.