In interactive dialogues, static modeling focuses on analyzing a current utterance to extract an elementary topic unit which is typically represented as a triple of core elements. This field is both novel and under-explored. Our research concentrates on customer service dialogues, which are typically concise but informative and noisy. It is challenging to distinguish the core elements from others. Moreover, as customer service dialogue data are scarce, efficient data utilization is also crucial. To address this, we introduce a Structure-Aware Boundary-Enhanced Span Classification Network (SABE) to extract elementary topic units effectively. Specifically, SABE uses a triple extraction module for extracting elementary topic units while it employs a structure-aware module and a boundary detection module to model the interrelations among core elements in a triple and detect their boundaries. Additionally, Focal Loss (FL) is introduced during the training phase to alleviate potential class imbalance. Experimental results on the Jingdong customer service dialogue dataset (JD dataset) highlight that SABE achieves state-of-the-art (SOTA) performance, notably improving elementary topic unit extraction by 1.02% over the previous best model.