00:00 - 17:0017:00 - 00:00
Prove the following result without using Urysohn's lemma.
$(X,\mathscr T)$ is normal and each closed subsets of $X$ is a $G_{\delta}$ set.Then, $(X,\mathscr T)$ perfectly normal.
My effort: I have proved using Urysohn's lemma. How do I prove without the use of Urysohn's lemma?
Let $A$ a...
In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size. In this sense, a measure is a generalization of the concepts of length, area, and volume. A particularly important example is the Lebesgue measure on a Euclidean space, which assigns the conventional length, area, and volume of Euclidean geometry to suitable subsets of the n-dimensional Euclidean space Rn. For instance, the Lebesgue measure of the interval [0, 1] in the real numbers is its length in the everyday sense of the word, specifically...
In mathematics, linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points.
== Linear interpolation between two known points ==
If the two known points are given by the coordinates
(
x
0
,
y
0
)
{\displaystyle (x_{0},y_{0})}
and
(
x
1
...
Here is a conjecture of mine:
If $G$ is the internal semidirect product of $N \unlhd G$ and $Q \le G$, and $\phi_1 : N' \to N$ and $\phi_2 : Q' \to Q$ are isomorphisms, then there is some $\theta : Q' \to \text{Aut } N'$ such that $G \cong N' \rtimes_\theta Q'$
My thought was to take $\the...
user131753
The problem with which I am struggling is the following,
Let $(P,\le)$ be a poset. If every chain and antichain of $P$ are of finite then $P$ is also finite.
My Attempt
Notice that by Hausdorff Maximality Principle every chain is contained in a maximal chain. By hypothesis the number of e...
Herbert Federer (July 23, 1920 – April 21, 2010) was an American mathematician. He is one of the creators of geometric measure theory, at the meeting point of differential geometry and mathematical analysis.
== Career ==
Federer was born July 23, 1920, in Vienna, Austria. After emigrating to the US in 1938, he studied mathematics and physics at the University of California, Berkeley, earning the Ph.D. as a student of Anthony Morse in 1944. He then spent virtually his entire career as a member of the Brown University Mathematics Department, where he eventually retired with the title of Professor...
00:00 - 17:0017:00 - 00:00
