Consider a Tychonoff space $X$ and $\beta X$ its Stone-$\check{\rm C}$ech compactification. I'm currently studying the existence of certain types of regular Borel measures on $X$. Since it's much simpler to obtain regular Borel meaures for a compact, I'd like to obtain them for $\beta X$, and then consider the restriction to $X$. To do so, I'd like to know whether $X$ is a Borel subset of $\beta X$.
2026-03-25 15:51:33.1774453893
Is $X$ a Borel subset of $\beta X$?
64 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in GENERAL-TOPOLOGY
- Is every non-locally compact metric space totally disconnected?
- Let X be a topological space and let A be a subset of X
- Continuity, preimage of an open set of $\mathbb R^2$
- Question on minimizing the infimum distance of a point from a non compact set
- Is hedgehog of countable spininess separable space?
- Nonclosed set in $ \mathbb{R}^2 $
- I cannot understand that $\mathfrak{O} := \{\{\}, \{1\}, \{1, 2\}, \{3\}, \{1, 3\}, \{1, 2, 3\}\}$ is a topology on the set $\{1, 2, 3\}$.
- If for every continuous function $\phi$, the function $\phi \circ f$ is continuous, then $f$ is continuous.
- Defining a homotopy on an annulus
- Triangle inequality for metric space where the metric is angles between vectors
Related Questions in BOREL-SETS
- Prove an assertion for a measure $\mu$ with $\mu (A+h)=\mu (A)$
- $\sigma$-algebra generated by a subset of a set
- Are sets of point convergence of Borel functions Borel?
- Can anyone give me an example of a measurable subset of the interval [10,100], that is not a Borel set.
- If $A \subseteq \mathbb{R}$ satisfies $m^\ast(A) = 0$, then there exist $B, C ∈ \mathcal{B}(\mathbb{R})$ such that $A = B \setminus C$?
- Why is the sigma algebra generated by the set of all closed subsets a subset of the Borel sigma algebra on $\mathbb{R}$?
- Permutation of binary expansion on (0,1)
- Kernel of finitely additive function on $\mathbf{N}$ and Borel sets
- Induced Borel $\sigma$-algebra.
- Does set with Lebesgue-Mass nonzero have almost surely an open subset
Related Questions in BOREL-MEASURES
- Versions of Lusin theorem
- Measure Theory Uncountable example with real line in $\sigma$ algebra
- Function is almost everywhere 1 w.r.t. sequence of Borel probability measures
- Is the Space of Borel Probability Measures over R connected?
- Permutation of binary expansion on (0,1)
- Measure theory sequence limsup
- $f^{-1}([-\infty,r))$ measurable for all rational numbers $r$
- A problem of measurable function in Cohn’s book.
- Uniqueness of measure by Laplace transformation
- Why is $\emptyset$ the only open null set?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
It need not be. I’ve not read the paper, but K.C. Goswami has a paper Density topology on R is not a Borel subset of its Stone-Čech compactification [PDF]. It uses results from Ichiro Amemiya, Susumu Okada, Yoshiaki Okazaki, Pre-Radon measures on topological spaces [PDF], which I have also not read.