This graduate thesis is designed in such a way that after we introduce all the terms and ”prepare” the ground for studying the larger properties we actually get important results. The first chapter deals generally with topology exits such as open sets, shutter, compactness, continuity, filters ... In the second chapter on a partially arranged set, with the help of its properties, it is studied when some set has the maximum element and comes to Zorn’s lemma and its consequences. Chapter 3 describes the creation of topology on the product, introduces projections, examines the properties of the product topology (compactness, separability, metrizability) and concludes that an index and a set of properties for the construction and properties of the product are also important. Although we have gone from a particular topological space, we conclude, in the end, that Hilbert’s cube, apart from the product, is actually a set of functions from a set of natural numbers at an interval of 0 to 1.