Weight properties in remainders and classes of spaces

A space X belongs to the class A if for any closed subspace Y of X the network weight nw(Y) is equal to the weight w(Y) of Y. One of the main results of the present article affirms that bX∖X∈A for any compactification bX of the paracompact p-space X. This fact contains a positive answer to one question of A.V. Arhangel'skii and A. Bella. For any Čech-complete space X the above result is not true. Any space with a point-countable k-base is a space from the class A.