Can banach spaces be taught without introducing the Metric space first?
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In our curriculum in france we dive head first in the topology of banach spaces probably to set a standing ground for approaching series and sequences of functions,integrable function(includes dependence on a parameter),power series.
and i was wondering whether there was a book that is compatible with our curriculum.
functional-analysis
asked Nov 20 at 19:18
Françoise Nicolas
185
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show 1 more comment
up vote
1
down vote
favorite
In our curriculum in france we dive head first in the topology of banach spaces probably to set a standing ground for approaching series and sequences of functions,integrable function(includes dependence on a parameter),power series.
and i was wondering whether there was a book that is compatible with our curriculum.
functional-analysis
asked Nov 20 at 19:18
Françoise Nicolas
185
I would say that learning about metric spaces before banach spaces is recommended. Many of the metric space topology results are used when proving theorems about Banach spaces
– rubikscube09
Nov 20 at 20:38
alright, but which book do you recommend?
– Françoise Nicolas
Nov 20 at 21:39
What topics are you familiar with? Assuming you are French, and have a solid real analysis background, I recommend "Functional Analysis, Sobolev Spaces and Partial Differential Equations" by Haim Brezis. The author (who is originally French) published a translation in English and it is very good. I am sure the French version is just as good if not better.
– rubikscube09
Nov 20 at 21:43
Interestingly enough you never need to talk about Cauchy sequences in Banach space theory. eg you can take as defintion of completeness the condition that a space is isomorphic to its bidual via the canonical map.
– s.harp
Nov 20 at 21:44
eh i think there is a misunderstanding,i'm a second year and this is our very first experience into "functional analysis" or whatever it is o.o so far we've only did calculus,some abstract algebra and linear algebra
– Françoise Nicolas
Nov 20 at 21:58
|
show 1 more comment
up vote
1
down vote
favorite
up vote
1
down vote
favorite
In our curriculum in france we dive head first in the topology of banach spaces probably to set a standing ground for approaching series and sequences of functions,integrable function(includes dependence on a parameter),power series.
and i was wondering whether there was a book that is compatible with our curriculum.
functional-analysis
asked Nov 20 at 19:18
Françoise Nicolas
185
In our curriculum in france we dive head first in the topology of banach spaces probably to set a standing ground for approaching series and sequences of functions,integrable function(includes dependence on a parameter),power series.
and i was wondering whether there was a book that is compatible with our curriculum.
functional-analysis
functional-analysis
asked Nov 20 at 19:18
Françoise Nicolas
185
asked Nov 20 at 19:18
Françoise Nicolas
185
asked Nov 20 at 19:18
Françoise Nicolas
185
asked Nov 20 at 19:18
Françoise Nicolas
185
asked Nov 20 at 19:18
Françoise Nicolas
185
185
I would say that learning about metric spaces before banach spaces is recommended. Many of the metric space topology results are used when proving theorems about Banach spaces
– rubikscube09
Nov 20 at 20:38
alright, but which book do you recommend?
– Françoise Nicolas
Nov 20 at 21:39
What topics are you familiar with? Assuming you are French, and have a solid real analysis background, I recommend "Functional Analysis, Sobolev Spaces and Partial Differential Equations" by Haim Brezis. The author (who is originally French) published a translation in English and it is very good. I am sure the French version is just as good if not better.
– rubikscube09
Nov 20 at 21:43
Interestingly enough you never need to talk about Cauchy sequences in Banach space theory. eg you can take as defintion of completeness the condition that a space is isomorphic to its bidual via the canonical map.
– s.harp
Nov 20 at 21:44
eh i think there is a misunderstanding,i'm a second year and this is our very first experience into "functional analysis" or whatever it is o.o so far we've only did calculus,some abstract algebra and linear algebra
– Françoise Nicolas
Nov 20 at 21:58
|
show 1 more comment
I would say that learning about metric spaces before banach spaces is recommended. Many of the metric space topology results are used when proving theorems about Banach spaces
– rubikscube09
Nov 20 at 20:38
alright, but which book do you recommend?
– Françoise Nicolas
Nov 20 at 21:39
What topics are you familiar with? Assuming you are French, and have a solid real analysis background, I recommend "Functional Analysis, Sobolev Spaces and Partial Differential Equations" by Haim Brezis. The author (who is originally French) published a translation in English and it is very good. I am sure the French version is just as good if not better.
– rubikscube09
Nov 20 at 21:43
Interestingly enough you never need to talk about Cauchy sequences in Banach space theory. eg you can take as defintion of completeness the condition that a space is isomorphic to its bidual via the canonical map.
– s.harp
Nov 20 at 21:44
eh i think there is a misunderstanding,i'm a second year and this is our very first experience into "functional analysis" or whatever it is o.o so far we've only did calculus,some abstract algebra and linear algebra
– Françoise Nicolas
Nov 20 at 21:58
I would say that learning about metric spaces before banach spaces is recommended. Many of the metric space topology results are used when proving theorems about Banach spaces
– rubikscube09
Nov 20 at 20:38
I would say that learning about metric spaces before banach spaces is recommended. Many of the metric space topology results are used when proving theorems about Banach spaces
– rubikscube09
Nov 20 at 20:38
alright, but which book do you recommend?
– Françoise Nicolas
Nov 20 at 21:39
alright, but which book do you recommend?
– Françoise Nicolas
Nov 20 at 21:39
What topics are you familiar with? Assuming you are French, and have a solid real analysis background, I recommend "Functional Analysis, Sobolev Spaces and Partial Differential Equations" by Haim Brezis. The author (who is originally French) published a translation in English and it is very good. I am sure the French version is just as good if not better.
– rubikscube09
Nov 20 at 21:43
What topics are you familiar with? Assuming you are French, and have a solid real analysis background, I recommend "Functional Analysis, Sobolev Spaces and Partial Differential Equations" by Haim Brezis. The author (who is originally French) published a translation in English and it is very good. I am sure the French version is just as good if not better.
– rubikscube09
Nov 20 at 21:43
Interestingly enough you never need to talk about Cauchy sequences in Banach space theory. eg you can take as defintion of completeness the condition that a space is isomorphic to its bidual via the canonical map.
– s.harp
Nov 20 at 21:44
Interestingly enough you never need to talk about Cauchy sequences in Banach space theory. eg you can take as defintion of completeness the condition that a space is isomorphic to its bidual via the canonical map.
– s.harp
Nov 20 at 21:44
eh i think there is a misunderstanding,i'm a second year and this is our very first experience into "functional analysis" or whatever it is o.o so far we've only did calculus,some abstract algebra and linear algebra
– Françoise Nicolas
Nov 20 at 21:58
eh i think there is a misunderstanding,i'm a second year and this is our very first experience into "functional analysis" or whatever it is o.o so far we've only did calculus,some abstract algebra and linear algebra
– Françoise Nicolas
Nov 20 at 21:58
|
show 1 more comment
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I would say that learning about metric spaces before banach spaces is recommended. Many of the metric space topology results are used when proving theorems about Banach spaces
– rubikscube09
Nov 20 at 20:38
alright, but which book do you recommend?
– Françoise Nicolas
Nov 20 at 21:39
What topics are you familiar with? Assuming you are French, and have a solid real analysis background, I recommend "Functional Analysis, Sobolev Spaces and Partial Differential Equations" by Haim Brezis. The author (who is originally French) published a translation in English and it is very good. I am sure the French version is just as good if not better.
– rubikscube09
Nov 20 at 21:43
Interestingly enough you never need to talk about Cauchy sequences in Banach space theory. eg you can take as defintion of completeness the condition that a space is isomorphic to its bidual via the canonical map.
– s.harp
Nov 20 at 21:44
eh i think there is a misunderstanding,i'm a second year and this is our very first experience into "functional analysis" or whatever it is o.o so far we've only did calculus,some abstract algebra and linear algebra
– Françoise Nicolas
Nov 20 at 21:58