In this paper,we first prove that the retract of a consonant space(or co-consonant space)is consonant(co-consonant).Simultaneously,we consider the co-consonance of two powerspace constructions and proved that(1)the co...In this paper,we first prove that the retract of a consonant space(or co-consonant space)is consonant(co-consonant).Simultaneously,we consider the co-consonance of two powerspace constructions and proved that(1)the co-consonance of the Smyth powerspace PS(X)implies the co-consonance of X if X is strongly compact;(2)the co-consonance of X implies the co-consonance of the Smyth powerspace under some conditions;(3)if the lower powerspace P_(H)(X)is co-consonant,then X is co-consonant;(4)for a continuous poset P,the lower powerspace P_(H)(ΣP)is co-consonant.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12331016)。
文摘In this paper,we first prove that the retract of a consonant space(or co-consonant space)is consonant(co-consonant).Simultaneously,we consider the co-consonance of two powerspace constructions and proved that(1)the co-consonance of the Smyth powerspace PS(X)implies the co-consonance of X if X is strongly compact;(2)the co-consonance of X implies the co-consonance of the Smyth powerspace under some conditions;(3)if the lower powerspace P_(H)(X)is co-consonant,then X is co-consonant;(4)for a continuous poset P,the lower powerspace P_(H)(ΣP)is co-consonant.
