Researches on breast cancer histopathological image classification have achieved a great breakthrough using deep backbones of Convolutional Neural Networks (CNNs) in recent years. However, due to the inductive bias of locality, CNNs are unable to effectively extract the global feature information of breast cancer histopathological images, limiting the improvement of the classification results. To overcome this shortcoming, this paper reasonably introduces an extra backbone stream of a pure transformer, which consists of a self-attention mechanism to capture global receptive fields of histopathological images, thereby compensating the locality characteristic of CNNs backbone. Based on two backbone streams of CNN and transformer, a dual-stream network called DCET-Net is proposed, which considers local features and global ones simultaneously, and progressively combines them from these two streams to form the final representations for classification. DCET-Net is extensively evaluated on the representative BreakHis histopathological image dataset, and experimental results demonstrate that it is highly competitive with the state-of-the-art CNN methods in breast cancer histopathological image classification task.