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nLab > Latest Changes: parameterized homotopy theory

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 1st 2019

    added pointer to

    diff, v9, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJun 20th 2022

    added pointer to:

    diff, v14, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJun 20th 2022
    • (edited Jun 20th 2022)

    added pointer to:

    diff, v14, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJun 20th 2022

    added pointer to:

    • Ioan Mackenzie James: Fibrewise topology, Cambridge Tracts in Mathematics, Cambridge University Press (1989) [[ISBN:9780521360906]]

    diff, v14, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 20th 2022

    Also added pointer to Booth & Brown.

    Then I sub-divided the list of references into “Exponential law for parameterized topological spaces” and references on parameterized homotopy theory proper.

    Finally I made the first of these lists an !include-file, since it is needed also elsewhere.

    As a result there is now a little overlap between the two lists. But that shouldn’t hurt.

    diff, v14, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJun 20th 2022

    I have recorded (in a new section, here) the definition of fiberwise mapping spaces and the fact that their construction preserves Hurewicz fibrations.

    diff, v15, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJun 20th 2022

    added the remark (here) that the fiberwise mapping space construction does not in general preserve weak Hausdorffness

    diff, v15, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJun 20th 2022

    made explicit (here) that the fiber of the fiberwise mapping space is the mapping space of the fibers

    diff, v16, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeJun 21st 2022

    added (here) the example

    Map(p B *X 0,p B *A 0)≃p B *Map(X 0,A 0) Map \big( p_B^\ast X_0 ,\, p_B^\ast A_0 \big) \;\simeq\; p_B^\ast Map\big(X_0,\, A_0\big)

    diff, v18, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeJun 21st 2022

    added (here) the statement that pullback of fiberwise mapping spaces exhibits a closed functor.

    diff, v19, current

1 to 10 of 10

  1.