locally compact Hausdorff spaces
1 Locally compact Hausdorff spaces
A locally compact Hausdorff space is a locally compact topological space (http://planetmath.org/LocallyCompact) with being a Hausdorff topology (http://planetmath.org/T2Space), that is, if given any distinct points , there exist disjoint sets such that, (that is, open sets), and with and satisfying the conditions that and .
An important, related concept to the locally compact Hausdorff space is that of a locally compact (topological) groupoid, which is a major concept for realizing extended quantum symmetries in terms of quantum groupoid representations in: quantum algebraic topology (QAT), topological QFT (TQFT), algebraic QFT (AQFT), axiomatic QFT, QCG, and quantum gravity (QG). This has also prompted the relatively recent development of the concepts of homotopy 2-groupoid and homotopy double groupoid of a Hausdorff space [1, 2]. It would be interesting to have also axiomatic definitions of these two important algebraic topology concepts that are consistent with the T2 axiom.
- 1 K.A. Hardie, K.H. Kamps and R.W. Kieboom., A homotopy 2-groupoid of a Hausdorff space, Applied Cat. Structures, 8 (2000): 209-234.
- 2 R. Brown, K.A. Hardie, K.H. Kamps and T. Porter, A homotopy double groupoid of a Hausdorff space, Theory and Applications of Categories 10,(2002): 71-93.
|Title||locally compact Hausdorff spaces|
|Date of creation||2013-03-22 18:19:24|
|Last modified on||2013-03-22 18:19:24|
|Last modified by||bci1 (20947)|
|Synonym||locally compact T2Space|
|Defines||locally compact topological space|