科研之友
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摘要
By [3], a frame L is pseudocompact if every %26lt;%26lt;-sequence in L joining to the top terminates. Here it is shown, for any completely regular L, that pseudocompactness is also equivalent to (i) the analogous condition for %26lt;-sequences, (ii) the countable almost compactness of L, (iii) the almost compactness of CozL as a sigma-frame and (iv) the condition that every countably based proper filter in L clusters. Further we establish the zero-dimensional counterparts of the above, concerning the integer valued notion of pseudocompactness. Finally, we add to this a characterization of pseudocompactness in terms of uniformities.
- 出版日期2013
