The most objective of this booklet is to offer a scientific remedy of singular homology and cohomology thought. it truly is in a few experience a sequel to the author's prior publication during this Springer-Verlag sequence entitled Algebraic Topology: An creation. This previous e-book is easily no longer a logical prerequisite for the current quantity. in spite of the fact that, it's going to definitely be valuable for a potential reader to have an acquaintance with a number of the themes taken care of in that previous quantity, equivalent to 2-dimensional manifolds and the funda psychological workforce. Singular homology and cohomology idea has been the topic of a few textbooks within the final couple of many years, so the fundamental define of the idea within reason good verified. for this reason, from the viewpoint of the maths concerned, there may be little that's new or unique in a booklet reminiscent of this. however, there's nonetheless room for loads of sort and originality within the information of the exposition. during this quantity the writer has attempted to offer a simple remedy of the subject material, stripped of all pointless definitions, terminology, and technical equipment. He has additionally attempted, anywhere possible, to stress the geometric motivation at the back of a number of the techniques.
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