摘要
This paper gives some topological propositions which are equivalent to the continuum hypothesis. The following results are also given: In the class of 1-st countable Hausdoff spaces, the existence of space which has calibre （ω<sub>1</sub>, ω） but no calibre ω<sub>1</sub> is equivalent to the existence of space which has calibre （ω<sub>1</sub>, ω） but is not point-countablely Lindelog, the existence of space which has calibre ω<sub>1</sub> but is not separable is equivalent to the existence of space which has calibre ω<sub>1</sub> but is not Lindelof, too.
This paper gives some topological propositions which are equivalent to the continuum hypothesis. The following results are also given: In the class of 1-st countable Hausdoff spaces, the existence of space which has calibre (ω_1, ω) but no calibre ω_1 is equivalent to the existence of space which has calibre (ω_1, ω) but is not point-countablely Lindelog, the existence of space which has calibre ω_1 but is not separable is equivalent to the existence of space which has calibre ω_1 but is not Lindelof, too.
