homeomorphic
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![**Theorem Statement:**
Prove the following: Let \( m \geq 3 \) be a positive integer, and let \(\{X_1, \ldots, X_m\}\) be an indexed collection of topological spaces. Then \(\prod_{i=1}^m X_i\) is homeomorphic to \(\left( \prod_{i=1}^{m-1} X_i \right) \times X_m\).
**Note the following definition:** We say that topological spaces \(X\) and \(Y\) are homeomorphic if and only if there is a homeomorphism
\[ h : X \to Y. \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff8d34f09-73ca-4440-9848-7d0d670a05c7%2F8e0338f4-8d13-460d-9a92-261eed2b71bf%2Ff73ey6q_processed.png&w=3840&q=75)
Transcribed Image Text:**Theorem Statement:**
Prove the following: Let \( m \geq 3 \) be a positive integer, and let \(\{X_1, \ldots, X_m\}\) be an indexed collection of topological spaces. Then \(\prod_{i=1}^m X_i\) is homeomorphic to \(\left( \prod_{i=1}^{m-1} X_i \right) \times X_m\).
**Note the following definition:** We say that topological spaces \(X\) and \(Y\) are homeomorphic if and only if there is a homeomorphism
\[ h : X \to Y. \]
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