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math.AT2026
Saturated directed spaces and generalized clocks
Philippe Gaucher
We construct a Hausdorff saturated directed space whose directed path space between two distinct points has nontrivial fundamental group although the corresponding trace space is a…
math.AT2026
Regular clock maps and trace spaces
Philippe Gaucher
A regular clock map is a regular map of directed spaces from a saturated directed space to the directed circle. We prove that the category of regular clock maps is a small-orthogon…