Topological and algebraic genericity of divergence and universality

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On dense-lineability of sets of functions on R (2009, background): “Gurariy also coined the following concept (which was also used in [4] under the name of algebraic genericity):”
Strong algebrability of sets of sequences and functions (2012, background): “In addition to algebrability, there exist other related properties such as lineability, dense-lineability and spaceability; see [3], [8], [9] and [14].”
Algebras in sets of queer functions (2007, unknown): “The algebraic structure of the set of such series has been investigated in [ 5 ] and in [6].”
Linear subsets of nonlinear sets in topological vector spaces (2013, background): “Finally, de la Rosa and Read [130] settled the problem in the negative, and several examples of hypercyclic operators T defined on classical spaces X and not satisfying the HCC have been provided by Bayart and Matheron in [51].”
Algebraic genericity of strict-order integrability (2010, background): “In this respect, let us recall some recent terminology introduced in [1], [3], [5] and [8].”
Lineability criteria, with applications (2013, background): “To this respect, let us recall some recent terminology introduced in [7], [12], [24] and [61].”
Abstract theory of universal series and applications (2008, methodology): “This has been done in [7], following the work of [5].”