Weakly infinite-dimensional spaces

In this survey article two new classes of spaces are considered: --spaces and ---spaces, . They are intermediate between the class of weakly infinite-dimensional spaces in the Alexandroff sense and the class of -spaces. The classes of --spaces and ---spaces coincide with the class of weakly infinite-dimensional spaces, while the compact --spaces are exactly the -compact spaces of Haver. The main results of the theory of weakly infinite-dimensional spaces, including classification via transfinite Lebesgue dimensions and Luzin-Sierpi?sky indices, extend to these new classes of spaces. Weak --spaces are characterised by means of essential maps to Henderson's -compacta. The existence of hereditarily -strongly infinite-dimensional spaces is proved.

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