symmetric monoidal (∞,1)-category of spectra
topology (point-set topology, point-free topology)
see also differential topology, algebraic topology, functional analysis and topological homotopy theory
Basic concepts
fiber space, space attachment
Extra stuff, structure, properties
Kolmogorov space, Hausdorff space, regular space, normal space
sequentially compact, countably compact, locally compact, sigma-compact, paracompact, countably paracompact, strongly compact
Examples
Basic statements
closed subspaces of compact Hausdorff spaces are equivalently compact subspaces
open subspaces of compact Hausdorff spaces are locally compact
compact spaces equivalently have converging subnet of every net
continuous metric space valued function on compact metric space is uniformly continuous
paracompact Hausdorff spaces equivalently admit subordinate partitions of unity
injective proper maps to locally compact spaces are equivalently the closed embeddings
locally compact and second-countable spaces are sigma-compact
Theorems
Analysis Theorems
Hilbert modular varieties are also called Hilbert modular surfaces.
(….)
Michael Atiyah, Harold Donnelly and Isadore Singer defined the signature defect of the boundary of a manifold as the eta invariant, the value at $s=0$ of their eta function, and used this to show that Hirzebruch’s signature defect of a cusp of a Hilbert modular variety can be expressed in terms of the value at $s=0$ or $s=1$ of a Shimizu L-function.
See also:
Last revised on May 8, 2024 at 14:56:49. See the history of this page for a list of all contributions to it.