The t-cat of a topological spaceMathworldPlanetmath X is the minimal number of open sets that cover X such that each open set in the cover has the homotopy typeMathworldPlanetmath of the unit circle S1. This means that for each open set U, the inclusion UiX is homotopicMathworldPlanetmath to some factorization UaS1bX, i.e.


When X is manifoldMathworldPlanetmath, this is related to the round complexity of X.


  • 1 D. Siersma, G. Khimshiasvili, On minimalPlanetmathPlanetmath round functions, Preprint 1118, Department of Mathematics, Utrecht University, 1999, pp. 18.
Title t-cat
Canonical name Tcat
Date of creation 2013-03-22 15:54:54
Last modified on 2013-03-22 15:54:54
Owner juanman (12619)
Last modified by juanman (12619)
Numerical id 7
Author juanman (12619)
Entry type Definition
Classification msc 55M30
Related topic RoundComplexity