# Weakly infinite-dimensional space

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A topological space such that for any infinite system of pairs of closed subsets of it,

there are partitions (cf. Partition) (between and ) such that . An infinite-dimensional space which is not weakly infinite dimensional is called strongly infinite dimensional. Weakly infinite-dimensional spaces are also called -weakly infinite dimensional. If in the above definition it is further required that some finite subfamily of the 's have empty intersection, one obtains the concept of an -weakly infinite-dimensional space.

#### References

 [1] P.S. Aleksandrov, B.A. Pasynkov, "Introduction to dimension theory" , Moscow (1973) (In Russian)