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Jun 2, 2021 at 17:24 comment added Jeff Strom @BenjaminSteinberg Moore paths and loops have real number lengths that are additive under products. In the Moore path and loop spaces, the basepoint is the unique trivial path, which has length zero.
Jun 2, 2021 at 13:05 comment added Benjamin Steinberg What is your base point in your example.? Do you put any algebraic constraints on the action or just topological? For example is every action of a discrete monoid on a discrete space a principal fibration? When I hear the word principal I would think you want a free action in an appropriate sense.
Jun 2, 2021 at 12:16 history edited Jeff Strom CC BY-SA 4.0
clarified pointed spaces
Jun 2, 2021 at 12:15 comment added Jeff Strom $X$ has a basepoint! Adding information...
Jun 2, 2021 at 12:03 comment added Benjamin Steinberg The terms weak orbits or connected components are used for what you can maximal orbit. I'm not sure how you get a sequence here. How does M map into X? Several points can be in the same orbit but not behave the same from the forward point of view.
Jun 2, 2021 at 11:34 history asked Jeff Strom CC BY-SA 4.0