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

... 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)

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