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## Search found 13 matches

Sat Sep 28, 2019 6:34 pm
Forum: Linear Algebra
Topic: Linear Projection
Replies: 2
Views: 1193

### Re: Linear Projection

$f=I$
Thu Mar 30, 2017 7:53 pm
Forum: Real Analysis
Topic: Series and continuous functions
Replies: 3
Views: 1064

### Re: Series and continuous functions

The first function is not continuous.(no Lebesgue integrable)

The condition 2 is not true.
The sequence must be decreasing
Thu Dec 15, 2016 11:21 pm
Forum: Number theory
Topic: Subset of natural numbers
Replies: 2
Views: 1750

### Re: Subset of natural numbers

Why there exist $a,b\in S$ with $(a,b)=1$?
Thu Dec 15, 2016 8:23 am
Forum: Real Analysis
Topic: Existence of $x$
Replies: 1
Views: 756

### Re: Existence of $x$

What if $\int _{A}g=0$ and $\int _{A}fg\neq 0$ ?
Thu Oct 27, 2016 2:14 pm
Forum: Real Analysis
Topic: Bounded sequence
Replies: 6
Views: 3007

### Re: Bounded sequence

It is not bounded near zero.
Thu Sep 08, 2016 2:05 pm
Forum: Algebra
Topic: $\mathbb{R}^5$ over $\mathbb{R}$
Replies: 2
Views: 1966

### Re: $\mathbb{R}^5$ over $\mathbb{R}$

We have
1)Every finite extension is algebraic
2)The algebraic closure of real numbers are
the complex numbers
3)Every finite extension of real numbers are
the complex numbers.
Mon Sep 05, 2016 10:50 pm
Forum: Algebra
Topic: An Interesting Exercise
Replies: 4
Views: 2236

### Re: An Interesting Exercise

1) subspace of a vector space for me( Rudin Functional Analysis and other) mean linear subspace.
2)This is a simple version of Tietze Extension Theorem.

0
Thu Sep 01, 2016 3:05 pm
Forum: Complex Analysis
Topic: Non existence of complex functions
Replies: 3
Views: 1474

### Re: Non existence of complex functions

If we restrict the function to the half-plane where ${\rm Re}(z) \geq 0$ , then $g$ is bounded which by a known fact of complex analysis means it is constant. The above is false. $g(z)=\exp(-z)$.
Thu Sep 01, 2016 2:24 pm
Forum: Complex Analysis
Topic: The function $f$ is constant
Replies: 2
Views: 1393

### Re: The function $f$ is constant

Is easy to prove:
The range of entire no constant function is dense.
Tue Aug 30, 2016 3:02 pm
Forum: Algebra
Topic: An Interesting Exercise
Replies: 4
Views: 2236

### Re: An Interesting Exercise

1) If X is compact then is not subspace
2)The functions in Hahn-Banach theorem are linear