Abstract
For a local po-space X and a base point x0 ∈ X, we define the universal dicovering space Π: X̃x0 → X. The image of Π is the future ↑ x0 of x0 in X and X̃x0 is a local po-space such that |π→ 1 (X̃, [x0], x1)| = 1 for the constant dipath [x0] ∈ Π-1(x0) and x1 ∈ X̃x0. Moreover, dipaths and dihomotopies of dipaths (with a fixed starting point) in ↑ x0 lift uniquely to X̃x0. The fibers Π-1(x) are discrete, but the cardinality is not constant. We define dicoverings P: X̂ → X x0 and construct a map φ: X̃x0 → X̂ covering the identity map. Dipaths and dihomotopies in X̂ lift to X̃x0, but we give an example where φ is not continuous.
Original language | English |
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Journal | Homology, Homotopy and Applications |
Volume | 5 |
Issue number | 2 |
Pages (from-to) | 1-17 |
Number of pages | 17 |
ISSN | 1532-0073 |
DOIs | |
Publication status | Published - 1 Jan 2003 |
Keywords
- Abstract homotopy theory
- Covering spaces
- Dihomotopy theory