Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorzskoda
    • CommentTimeNov 29th 2009

    It seems to me that despite so lenghty discussions and entry related to the mapping space-hm adjunction, only the ideal situations are treated (convenient categories of spaces). For this reason, I have created a new entry exponential law for spaces containing the conditions usually used in the category of ALL topological spaces, as well as few remarks about the pointed spaces.

    • CommentRowNumber2.
    • CommentAuthorTobyBartels
    • CommentTimeNov 29th 2009

    Thanks, that's good to know.

    One bit wasn't clear to me, so I asked a question.

    Also, I changed \theta' to \theta_*, which made sense to me; sorry if that's wrong.

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeNov 29th 2009

    I added some further details on top of the article, since the exponentiability in Top was not fully addressed. A useful reference has been added.

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeNov 30th 2009
    • (edited Nov 30th 2009)

    It is OK to write theta with lower star, but this lower star is not induced by functoriality, but by a bit more explicit/careful consideration.

    • CommentRowNumber5.
    • CommentAuthorTodd_Trimble
    • CommentTimeNov 30th 2009

    I put a query over at locally compact space, although I think I already know the answer.

    • CommentRowNumber6.
    • CommentAuthorTobyBartels
    • CommentTimeDec 4th 2009

    There are many definitions of locally compact spaces in the literature, all equivalent for Hausdorff spaces, and it's difficult to untangle them. The page exponential law for spaces suggests that core-compactness is the deciding feature. Do we know enough to be Bourbaki and decide which is best?

    • CommentRowNumber7.
    • CommentAuthorTodd_Trimble
    • CommentTimeDec 4th 2009

    Yes, I believe so: the topology should be a continuous lattice, which means we should opt for the definition that says that compact neighborhoods of a point are a neighborhood basis, for every point. I may add that in in a bit.

    • CommentRowNumber8.
    • CommentAuthorMike Shulman
    • CommentTimeMay 4th 2010

    I did some reorganizing of exponential law for spaces, and added a reference to Claudio Pisani’s neat result characterizing exponentiable spaces in terms of ultrafilter convergence.