Exponential density vs exponential domination

It is established that a space X with exponentialκ-domination has density not exceeding κ if l(X) ≤ κ and t(X) ≤ κ. We also introduce a weakerproperty called exponentialκ-density and show thatit behaves nicely under standard operations. It is proved thatexponential κ-density is preserved by continuous images,open subspaces, arbitrary products and extensions. Just likeexponential κ-domination, exponential κ-density ofX implies that κ+ is a caliber of X; every dyadiccompact space must have exponential ø -density while spaceswith exponential κ-density and π-character notexceeding 2 κ have density ≤ κ. Inmonotonically normal spaces, exponential κ-densitycoincides with density ≤ κ while under the hypothesis2 κ= κ+, it follows from s(X) ≤ κ thatd(X) ≤ κ whenever X is a space with exponentialκ-density.