Delta-generated space



A Δ\Delta-generated space is a topological space XX whose topology is the final topology induced by all maps Δ nX\Delta^n \to X, where Δ n\Delta^n runs over all the standard simplices.


The category of Δ\Delta-generated spaces is coreflective in Top. It is also locally presentable, and supports a model structure. Thus, it is a nice category of spaces.


Δ\Delta-generated spaces were originally proposed by Jeff Smith as a nice category of spaces for homotopy theory. A proof that they are locally presentable is in:

See also at directed homotopy theory.

Other references include:

Revised on July 30, 2015 18:43:51 by Urs Schreiber (