Munkres Topology - Chapter 7 - Complete Metric Spaces and Function Spaces

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Reading Chapter 7 of Munkres on Complete Metric Spaces and Function Spaces is feasible without prior completion of the Tietze Extension Theorem, the Imbeddings of Manifolds section, and Chapters 5 and 6. Familiarity with concepts up to the Urysohn Metrization Theorem is sufficient to begin. It is advisable to consult the index for any unfamiliar terms encountered during reading. Engaging with the material directly and addressing gaps in understanding as they arise is a common approach in studying mathematics. Starting the chapter is encouraged, as it allows for a more hands-on learning experience.
sammycaps
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Hello, I was wondering if it was possible (or advisable) to read Chapter 7 of Munkres (Complete Metric Spaces and Function Spaces) without having done Tietze Extension Theorem, the Imbeddings of Manifolds section, the entirety of Chapter 5 (Tychonoff Theorem) and the entirety of Chapter 6 (Metrization Theorems and Paracompactness)? I've done everything through The Urysohn Metrization Theorem (which is nearly the end of Chapter 4, right before Tietze Extension Theorem).

I expect the exercises might have some stuff from these areas, but flipping through the text quickly it *seems* I should be alright. But, I don't know. Any suggestions are welcome.

Thanks!
 
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I suggest you just start doing it, and if you come across some terms you don't understand, look them up in the index, get a handle on them, then return to where you were. You may have to recurse a few levels. That's how everybody reads math books anyway.
 
Tinyboss said:
I suggest you just start doing it, and if you come across some terms you don't understand, look them up in the index, get a handle on them, then return to where you were. You may have to recurse a few levels. That's how everybody reads math books anyway.

Alright, thanks!
 

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