Applications of elementary submodels in topology

The purpose of this thesis is to investigate a topological construction using elementary submodels. In the second chapter, the construction is used to obtain some results on realcompactness and completeness. More interestingly, the construction is used to prove the separable case of Nikiel's conjecture that a space is compact and monotonically normal if and only if it is the continuous image of some compact, linearly ordered space. This result is originally due to M.E. Rudin by a more difficult method.