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  • 1 Universidade de São Paulo Instituto de Matemática e Estatística Caixa Postal 66281 05311-970 São Paulo Brasil
  • | 2 Universidad Autónoma Metropolitana Departamento de Matemáticas Av. San Rafael Atlixco, 186, Col. Vicentina, Iztapalapa C.P. 09340 México, D.F. México
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This is a sequel of the work done on (strongly) monotonically monolithic spaces and their generalizations. We introduce the notion of monotonically κ-monolithic space for any infinite cardinal κ and present the relevant results. We show, among other things, that any σ-product of monotonically κ-monolithic spaces is monotonically κ-monolithic for any infinite cardinal κ; besides, it is consistent that any strongly monotonically ω-monolithic space with caliber ω1 is second countable. We also study (strong) monotone κ-monolithicity in linearly ordered spaces and subspaces of ordinals.