A note on the connectedness property of union-free generic sets of partial orders
This is an incremental contribution that clarifies a theoretical property in the context of data depth functions for partial orders, primarily relevant to researchers in order theory and formal concept analysis.
The paper proves a connectedness property for union-free generic sets of partial orders, originally introduced in prior work on data depth functions, by leveraging formal concept analysis to provide a structural insight.
This short note describes and proves a connectedness property which was introduced in Blocher et al. [2023] in the context of data depth functions for partial orders. The connectedness property gives a structural insight into union-free generic sets. These sets, presented in Blocher et al. [2023], are defined by using a closure operator on the set of all partial orders which naturally appears within the theory of formal concept analysis. In the language of formal concept analysis, the property of connectedness can be vividly proven. However, since within Blocher et al. [2023] we did not discuss formal concept analysis, we outsourced the proof to this note.