12 citations · 63 across the 29 of their papers we have counts for
4 papers · 1 filter
On the Topology of Metric Spaces definable in o-minimal expansions of fields
Erik Walsberg
We study the topology of metric spaces which are definable in o-minimal expansions of ordered fields. We show that a definable metric space either contains an infinite definable di…
Isometric Embeddability of Snowflakes
Erik Walsberg
We show that a snowflake of a metric space with positive Hausdorff dimension does not admit an isometric embedding into euclidean space.
Tame Topology over Dp-minimal Structures
Pierre Simon, Erik Walsberg
We develop tame topology over dp-minimal structures equipped with definable uniformities satisfying certain assumptions. Our assumptions are enough to ensure that definable sets ar…
Dp-minimal valued fields
Franziska Jahnke, Pierre Simon, Erik Walsberg
We show that dp-minimal valued fields are henselian and that a dp-minimal field admitting a definable type V topology is either real closed, algebraically closed or admits a non-tr…