# Weakly infinite-dimensional space

A topological space \$X\$ such that for any infinite system of pairs of closed subsets \$(A_i,B_i)\$ of it, \$\$ A_i \cap B_i = \emptyset,\ \ i=1,2,\ldots \$\$ there are partitions \$C_i\$ (between \$A_i\$ and \$B_i\$) such that \$\cap C_i = \emptyset\$. An infinite-dimensional space which is not weakly infinite dimensional is called strongly infinite dimensional. Weakly infinite-dimensional spaces are also called \$A\$-weakly infinite dimensional. If in the above definition it is further required that some finite subfamily of the \$C_i\$ have empty intersection, one obtains the concept of an \$S\$-weakly infinite-dimensional space.

#### References

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