第一可数正则空间的闭扩充

Closed Extensions of First Countable Regular Spaces

证明了第一可数正则闭空间、第一可数正则极小空间与第一可数正则弱紧空间的等价性,并进一步证明了每一个局部弱紧的第一可数正则空间一定存在一个第一可数正则闭扩充.

We prove that equivalance of first countable regular-closed spaces and minimal first countable regular spaces and feebly compact first countable regular spaces. We also prove that there exists a first countable regular-closed extension space for every locally feebly compact first countable regular space.