Dicovering spaces

Lisbeth Fajstrup*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

17 Citations (Scopus)

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 languageEnglish
JournalHomology, Homotopy and Applications
Volume5
Issue number2
Pages (from-to)1-17
Number of pages17
ISSN1532-0073
DOIs
Publication statusPublished - 1 Jan 2003

Keywords

  • Abstract homotopy theory
  • Covering spaces
  • Dihomotopy theory

Fingerprint

Dive into the research topics of 'Dicovering spaces'. Together they form a unique fingerprint.

Cite this