Compactly Generated

In mathematics, compactly generated can refer to:

  • compactly generated group
  • compactly generated space

Other articles related to "compactly generated, generated":

Compactly Generated Space - Examples
... Most topological spaces commonly studied in mathematics are compactly generated ... Every compact space is compactly generated ... Every locally compact space is compactly generated ...
Compactly Generated Group
... In mathematics, a compactly generated (topological) group is a topological group G which is algebraically generated by one of its compact subsets ... (widely used in algebraic topology) of a compactly generated space -- one whose topology is generated (in a suitable sense) by its compact subspaces ...
Compactly Generated Space - Properties
... We denote CGTop the full subcategory of Top with objects the compactly generated spaces, and CGHaus the full subcategory of CGTop with objects the Hausdorff separated spaces ... Given any topological space X we can define a (possibly) finer topology on X which is compactly generated ... It follows that Xc is compactly generated ...
CW Complex - Properties
... On the other hand, the product of X and Y in the category of compactly generated spaces agrees with the weak topology and therefore defines a CW-complex ... Note that X and Y are compactly generated Hausdorff spaces, so Hom(X,Y) is often taken with the compactly generated variant of the compact-open topology the above statements remain true ...

Famous quotes containing the word generated:

    It is precisely the purpose of the public opinion generated by the press to make the public incapable of judging, to insinuate into it the attitude of someone irresponsible, uninformed.
    Walter Benjamin (1892–1940)