Założenia problematyki nieskończoności wszechświata w kosmologii Robertsona-Walkera

The assumptions of the problem of the infinity in Robertson- Walker’ s Cosmology are discussed. The very concept of the infinity is defined by means of the topological and metrical terms. With reference to the Universe it is understood as the infinity in time and space. The main assumptions in the approach to the infinity of the Universe in Robertson-Walker's Cosmology are: homogeneity of space and time, their relational conception as well as their topological and metrical structures. Because of these assumptions the question remains open - is the actual Universe finite or not?