A simultaneous localisation and mapping (SLAM) algorithm for topological maps is proposed. Especially, this algorithm deals with a semi-permanent dynamics induced by door opening and closing. To deal with the semi-permanent dynamics, nodes are classified into two types. One is an invariant node that is free from the dynamics, and the other is a variant node that is not affected by door opening and closing. Two different approaches are used at the same time: a quasi-static SLAM for the invariant nodes and a dynamic SLAM for the variant nodes. A gross shape of the given environment is represented by the quasi-static SLAM algorithm, and a detailed shape of the environment is revealed via the dynamic SLAM. Experimental results validate that the proposed algorithm produces a topologically consistent map under the semi-permanent dynamics.