![5 Questions on Midterm Exam on Product Topology of Continuous Map | MATH 531 | Exams Topology | Docsity 5 Questions on Midterm Exam on Product Topology of Continuous Map | MATH 531 | Exams Topology | Docsity](https://static.docsity.com/documents_first_pages/2009/07/23/a381563b7f97253fd6b50e34d782fee2.png)
5 Questions on Midterm Exam on Product Topology of Continuous Map | MATH 531 | Exams Topology | Docsity
Introduction to Algebraic Topology (Part 1) Professor Anant R Shastri Department of Mathematics Indian Institute of Technology B
![SOLVED: 5. The following statements are independent. Prove each one. (a) X has the discrete topology. Prove that any map f: X â†' Y is continuous. (b) Let A ∈ X and SOLVED: 5. The following statements are independent. Prove each one. (a) X has the discrete topology. Prove that any map f: X â†' Y is continuous. (b) Let A ∈ X and](https://cdn.numerade.com/ask_images/5255a69db25d4b3b89a684df6a8ceca3.jpg)
SOLVED: 5. The following statements are independent. Prove each one. (a) X has the discrete topology. Prove that any map f: X â†' Y is continuous. (b) Let A ∈ X and
![SOLVED: 2) Prove that the identity map from a topological space to itself is continuous. 3) Prove that the composition of continuous functions is continuous. Consider the function f(r) = 2r as SOLVED: 2) Prove that the identity map from a topological space to itself is continuous. 3) Prove that the composition of continuous functions is continuous. Consider the function f(r) = 2r as](https://cdn.numerade.com/ask_previews/d6ee53cf-db48-46f2-8ec7-8f55e67781e0_large.jpg)
SOLVED: 2) Prove that the identity map from a topological space to itself is continuous. 3) Prove that the composition of continuous functions is continuous. Consider the function f(r) = 2r as
![Map (mathematics): Synonym, Partial function, Injective function, Continuous function, Topology, Linear map, Serge Lang, Bijection, injection and surjection : Miller, Frederic P., Vandome, Agnes F., McBrewster, John: Amazon.it: Libri Map (mathematics): Synonym, Partial function, Injective function, Continuous function, Topology, Linear map, Serge Lang, Bijection, injection and surjection : Miller, Frederic P., Vandome, Agnes F., McBrewster, John: Amazon.it: Libri](https://m.media-amazon.com/images/I/71Z70Z51RYL._AC_UF1000,1000_QL80_.jpg)