A May-type spectral sequence for higher topological Hochschild
... ring (rather than a filtered commutative ring spectrum), M. Brun constructed a spectral sequence of the form 1.0.1 in the paper [8]. In Theorem 2.9 of the preprint [3], V. Angeltveit remarks that a version of spectral sequence 1.0.1 exists for commutative ring spectra by virtue of a lemma in [8] on ...
... ring (rather than a filtered commutative ring spectrum), M. Brun constructed a spectral sequence of the form 1.0.1 in the paper [8]. In Theorem 2.9 of the preprint [3], V. Angeltveit remarks that a version of spectral sequence 1.0.1 exists for commutative ring spectra by virtue of a lemma in [8] on ...
SimpCxes.pdf
... for most purposes of basic algebraic topology. There are more general classes of spaces, in particular the finite CW complexes, that are more central to the modern development of the subject, but they give exactly the same collection of homotopy types. The relevant background on simplicial complexes ...
... for most purposes of basic algebraic topology. There are more general classes of spaces, in particular the finite CW complexes, that are more central to the modern development of the subject, but they give exactly the same collection of homotopy types. The relevant background on simplicial complexes ...
Shortest paths and geodesics
... Example 2.2.2 (Length space). The Euclidean space E n is a length space. As seen in Proposition 2.2.1 the shortest path in dI (x, y) is a straight line between x and y and in this case the Euclidean metric d(x, y) coincides with dI (x, y). Example 2.2.3 (Length space). The sphere S1 ⊂ R2 with the Eu ...
... Example 2.2.2 (Length space). The Euclidean space E n is a length space. As seen in Proposition 2.2.1 the shortest path in dI (x, y) is a straight line between x and y and in this case the Euclidean metric d(x, y) coincides with dI (x, y). Example 2.2.3 (Length space). The sphere S1 ⊂ R2 with the Eu ...
A CROSS SECTION THEOREM AND AN APPLICATION TO C
... to B, is open, tt(B) = J, and yet there is no Borel cross section (in this case, there is no Borel uniformization). Recall that if F is a subset of A" X Y, then a uniformization of F is a subset F of E such that Ex ^= 0 if and only if Fx consists of exactly one point, where Ex = [y\(x, y) is in E]. ...
... to B, is open, tt(B) = J, and yet there is no Borel cross section (in this case, there is no Borel uniformization). Recall that if F is a subset of A" X Y, then a uniformization of F is a subset F of E such that Ex ^= 0 if and only if Fx consists of exactly one point, where Ex = [y\(x, y) is in E]. ...
175 ALMOST NEARLY CONTINUOUS MULTIFUNCTIONS 1
... The class of nearly compact spaces is properly placed between the classes of quasi-H-closed (i. e., almost compact) spaces and the spaces satisfying the finite chain condition, i. e., every space satisfying the finite chain condition is nearly compact and every nearly compact space is almost compact ...
... The class of nearly compact spaces is properly placed between the classes of quasi-H-closed (i. e., almost compact) spaces and the spaces satisfying the finite chain condition, i. e., every space satisfying the finite chain condition is nearly compact and every nearly compact space is almost compact ...