On $\Delta$-generated and compactly generated topological spaces:
On model structures on topological spaces and the notion of $\Delta$-Hausdorff $\Delta$-generated space (a natural separation condition for $\Delta$-generated spaces):
On directed homotopy theory and higher dimensional transition systems:
Philippe Gaucher, Directed algebraic topology and higher dimensional transition system, New-York Journal of Mathematics 16 (2010), 409 - 461 (arxiv:0903.4276)
Philippe Gaucher, Towards a homotopy theory of higher dimensional transition systems, Theory and Applications of Categories, Vol. 25, No. 12, 2011, pp. 295–341 (arxiv:1011.0918)
On left-determined model categories:
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