| The countable compactness holds important status in general topological spaces. And it has some interesting properties. Also, the countable compactness holds important status in fibrewise topological spaces, accordingly it has some interesting properties. Combined with the analysis of the existed countable compactness, locally countable compactness and their correlative properties, our paper discussed in fibrewise topological spaces the conception of point-fibrewise countable compact spaces, fibrewise countable compact spaces , fibrewise locally countable compact spaces and their correlative properties. Besides the conditions which the morphism should satisfy to preserve (inversely preserve) point-fibrewise countable compactness, fibrewise countable compactness, fibrewise locally countable compactness in the category (the objects are the fibrewise topological spaces over different bases, for two objects a morphism from X to Y is a pair of continuous maps such thatλ·p = q·f ). |
