6533b830fe1ef96bd1297bc5
RESEARCH PRODUCT
Lifting paths on quotient spaces
L.b. TreybigD. DanielJ. NikielE. D. TymchatynH. Murat Tuncalisubject
CombinatoricsDecompositionPure mathematicsImage (category theory)Null familyOrdered continuumBoundary (topology)Geometry and TopologyElement (category theory)Quotient space (linear algebra)QuotientLifting images of arcsMathematicsdescription
Abstract Let X be a compactum and G an upper semi-continuous decomposition of X such that each element of G is the continuous image of an ordered compactum. If the quotient space X / G is the continuous image of an ordered compactum, under what conditions is X also the continuous image of an ordered compactum? Examples around the (non-metric) Hahn–Mazurkiewicz Theorem show that one must place severe conditions on G if one wishes to obtain positive results. We prove that the compactum X is the image of an ordered compactum when each g ∈ G has 0-dimensional boundary. We also consider the case when G has only countably many non-degenerate elements. These results extend earlier work of the first named author in a number of ways.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2009-05-01 | Topology and its Applications |