Understanding Theorems: Open Mapping & Closed Range

[Miss_lolitta]

Miss. Lolitta says:

Hello everybody here

Can someone give me a complete lecture-that has introduction & examples and explaining-for

"the open mapping theorem" and "the closed range theorem"

actually I read some books about this theorem but they weren't clear for me

please,help me to figure out this theorem..

Thanks in advance

 

[mannyfold]

Hi,

I'm not familiar with the theorems, but I can give a few definitions:

f is an open mapping if for all open sets O in the domain, f(O) is open in the range. In other words, f maps open sets to open sets.

f is a closed mapping if for all closed sets C in the domain, f(C) is closed in the range. In other words, f maps closed sets to closed sets.

I'm not sure what theorems you are talking about.

 

[HallsofIvy]

Try these:
http://en.wikipedia.org/wiki/Open_mapping_theorem
http://mathworld.wolfram.com/OpenMappingTheorem.html
http://whyslopes.com/etc/Real-Analysis-Decimal-View/appF1-Closed-Range-Theorem.html

 

[Miss_lolitta]

thanks sooooooo much

 

[JonF]

Try these:
http://en.wikipedia.org/wiki/Open_mapping_theorem
Range-Theorem.html[/url]

I think I should just send tuition money to wikipedia instead of my university.