Differential geometty and topology are the areas of higher mathematics, which particularly require visual representation of studying objects for better understanding of the material. On the other hand, the complex structure of such objects niakes their visualization a challenge for modern graphical systems. In this paper we describe some methods useful for adequate representation of topologically non-trivial objects in virtual environment systems, particularly the acceleration of standard mechanisms for rendering of transparent surjiaces, applicable for complex cases of self-intersecting time-dependent surjaces, not necessarily admitting continuous jields of normal vectors. We also use a simple technique of image-based rendering, which places stereo-photographs of real environments as static background for 3 0 virtual scenes. The methods are iniplemented in educational application, which demonstrates the ntain properties of elementary topological objects (Moebius band, Klein bottle, projective plane etc) and gives a possihiliq to explore interactively the complex constructions, arising in higher mathematics.