Generalization is a fundamental mathematical practice across all disciplines and content areas (Amit & Klass, 2005; Lannin, 2005; Pierce, 1902; Vygotsky, 1986; Ellis, Lockwood, Tillema & Moore, 2017). While a considerable amount of research has been conducted on students' generalizing activity in algebraic contexts (Amit & Klass 2005; Becker &...
The classical dimension theories of Menger-Urysohn and Lebesgue are equivalent on metric spaces. However, their infinite-dimensional analogues may differ, even on compact metric spaces. The three such infinite-dimensional dimension theories considered in this thesis are known as countable-dimensionality, property C, and weak infinite-dimensionality. The open questions regarding the relationships between...