I'm interested in lattice-theoretic properties of the algebra of open sets in a subspace of the Baire space $\Bbb N^{\Bbb N}$ can or cannot have. What is a good source on this matter? (An Internet search like "locale Polish space" did not reveal much.)
2026-02-23 02:50:26.1771815026
Reference request: lattice theory of the algebra of open sets in a subspace of the Baire space
104 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated 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 REFERENCE-REQUEST
- Best book to study Lie group theory
- Alternative definition for characteristic foliation of a surface
- Transition from theory of PDEs to applied analysis and industrial problems and models with PDEs
- Random variables in integrals, how to analyze?
- Abstract Algebra Preparation
- Definition of matrix valued smooth function
- CLT for Martingales
- Almost locality of cubic spline interpolation
- Identify sequences from OEIS or the literature, or find examples of odd integers $n\geq 1$ satisfying these equations related to odd perfect numbers
- property of Lebesgue measure involving small intervals
Related Questions in LATTICE-ORDERS
- When a lattice is a lattice of open sets of some topological space?
- How to identify if a given Hasse diagram is a lattice
- How to find the smallest cardinal of a minimal generating set of a lattice
- Finding a poset with a homogeneity property
- Why is the "distributive lattice" structure of domino tilings significant?
- Two lattice identities
- Quickly determining whether given lattice is a distributive lattice from a given Hasse diagram
- Characteristic of a lattice that subsets contain their meets and joins
- Equalities in Heyting algebras
- Show that $(\operatorname{Up}(P),\subset)$ is a distributive lattice
Related Questions in DESCRIPTIVE-SET-THEORY
- Are compact groups acting on Polish spaces essentially Polish?
- For any countable ordinal $\alpha$, there is some closed set of reals whose Cantor-Bendixson rank is $\alpha$
- how to construct a rudimentary function $h$ used in the paper ''scales in $L(\mathbb{R})$''
- Under $MA+\neg CH$ there exists a $Q$-set.
- Separating closed sets in the bubble space. (a.k.a Moore plane a.ka. Niemytzki plane.)
- Precision on the Baire property
- Uniqueness in Baire property representation for compact Hausdorff spaces
- Can height of tree more than $\aleph_0$
- Example of a unit circle subset that is $F_{\sigma\delta}$ but not $F_\sigma$
- Finite approximations to transfinite sums of real numbers.
Related Questions in THE-BAIRE-SPACE
- A Homeomorphism Between the Baire Space and a Countable $G_\delta$ set of the Cantor Space
- Gale-Stewart game
- Baire Space and Its Equivalent Property
- The Baire space as an automorphism group?
- Two Baire measure, $\left\{A\subseteq X: A \text{ Baire set}\ \mu(A)=\nu(A)\right\}$ is $\sigma$-algebra
- $S_\infty$ is a non-locally compact Polish group (Kechris)
- Baire space $\mathbb{N}^\mathbb{N}$ written as $\mathbb{R}$
- What can I say about $A^{c}$ if $A$ is not open
- $H$ thin in $X$ implies that $X\setminus H$ contains a generic subset
- Let $X$ be a complete metric space. $E$ is a non empty open set in $X$ Then is $E$ a first category set or second category 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?