Algebraic topology: a first course by Marvin J. Greenberg

By Marvin J. Greenberg

Great first booklet on algebraic topology. Introduces (co)homology via singular theory.

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Thank you anon for the djvu add, I simply switched over and did ocr with tesseract. I didn't like Munkres kind (too verbose imo) this one is far better.

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when i used to be a pupil, this and Munkres have been the topology books opposed to which each and every different e-book was once measured.

And whereas Munkres used to be of a extra introductory taste, this was once the true deal.


There are just a number of vintage encyclopaedic texts on undergraduate topology, and Dugundji's is one in every of them. And between such books, this is often my favorite as the others are too out of date or too voluminous. Dugundji's publication is brief, smooth, and impeccable. It covers each subject an undergraduate may still be aware of or even extra. it truly is nonetheless necessary for me after years of use. It exposes all vital options of set topology and offers a quick yet concentrated creation to algebraic topology.
You won't remorse to learn it.


One of the simplest Topology books i've got learn. even supposing the publication has no figures (as one may anticipate from a topology book), nearly each element is roofed and there aren't imprecise elements within the proofs. for instance, the publication through Willard can be reliable, yet in a few components there are extra advanced info left for the reader. I took a uncomplicated topology graduate point direction at the first half 2007, which consisted on fixing the issues during this publication. We have been capable of finding a few difficulties that requested to turn out whatever fake, yet they have been 3 or 4 between the entire difficulties from sections III to VIII. besides, this e-book is a vintage so you might personal in the event you plan to paintings in topology or at the least learn it whereas learning the topic. It's only a disgrace that the booklet is out of print.

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Example text

5) is entirely evaluated in Rn and does no longer refer to M itself. This suggest to build topological manifolds by patching together local charts provided the changes of coordinates satisfy the cocycle condition. This is indeed possible by the following construction: Let I be an index set and let Vi ⊆ Rn be non-empty and open for i ∈ I . Moreover, let Vi j ⊆ V j be an open subset for every pair i = j. 6) ϕi j : Vi j −→ V ji In particular, we require Vi j = ∅ iff V ji = ∅. It will be useful to set Vii = Vi and ϕii = idVi for all i ∈ I .

Indeed, for O ⊆ M open the preimage of O is ι−1 (O) = N ∩ O which is open in N by the very definition of the subspace topology. Moreover, ι is clearly a bijection onto its image. Finally, the homeomorphism property is clear by the very definition. This example is the prototype of an embedding and motivates the name. 8 Let f : (M, M) −→ (N , N ) be a map between topological spaces. Then the following statements are equivalent: 24 (i) (ii) (iii) (iv) 2 Topological Spaces and Continuity The map f is a homeomorphism.

9 (Closures, open interiors, and boundaries) Find and describe examples of topological spaces (M, M) and subsets A, B ⊆ M for the following statements: (i) The boundary of the boundary of a subset can but needs not to be empty. (ii) Let A ⊆ B. Show that the following three situations are possible: a strict inclusion ∂ A ⊆ ∂ B, a strict inclusion ∂ B ⊆ ∂ A, a trivial intersection ∂ A∩∂ B = ∅ with both boundaries being non-empty. (iii) The open interior of a union A ∪ B can be strictly larger than the union of the open interiors A◦ ∪ B ◦ .

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