What is the quotient space $S^{2}\times S^{2}\times S^{2}/\sim$ topologically, geometrically, and algebraically, where $S^{2}\subset\mathbb{R}^{3}$ is the unit sphere of $\mathbb{R}^{3}$ and the equivalence relation is defined as $$\left(p_{1},p_{2},p_{3}\right)\sim\left(p'_{1},p'_{2},p'_{3}\right)$$ iff there exists $T\in O(3)$ such that $$T\left(p_{1},p_{2},p_{3}\right)=\left(p'_{1},p'_{2},p'_{3}\right)?$$ Thanks.
2026-03-27 10:07:29.1774606049
What is this quotient space?
111 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in ABSTRACT-ALGEBRA
- Feel lost in the scheme of the reducibility of polynomials over $\Bbb Z$ or $\Bbb Q$
- Integral Domain and Degree of Polynomials in $R[X]$
- Fixed points of automorphisms of $\mathbb{Q}(\zeta)$
- Group with order $pq$ has subgroups of order $p$ and $q$
- A commutative ring is prime if and only if it is a domain.
- Conjugacy class formula
- Find gcd and invertible elements of a ring.
- Extending a linear action to monomials of higher degree
- polynomial remainder theorem proof, is it legit?
- $(2,1+\sqrt{-5}) \not \cong \mathbb{Z}[\sqrt{-5}]$ as $\mathbb{Z}[\sqrt{-5}]$-module
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 GEOMETRY
- Point in, on or out of a circle
- Find all the triangles $ABC$ for which the perpendicular line to AB halves a line segment
- How to see line bundle on $\mathbb P^1$ intuitively?
- An underdetermined system derived for rotated coordinate system
- Asymptotes of hyperbola
- Finding the range of product of two distances.
- Constrain coordinates of a point into a circle
- Position of point with respect to hyperbola
- Length of Shadow from a lamp?
- Show that the asymptotes of an hyperbola are its tangents at infinity points
Related Questions in LIE-GROUPS
- Best book to study Lie group theory
- Holonomy bundle is a covering space
- homomorphism between unitary groups
- On uniparametric subgroups of a Lie group
- Is it true that if a Lie group act trivially on an open subset of a manifold the action of the group is trivial (on the whole manifold)?
- Find non-zero real numbers $a,b,c,d$ such that $a^2+c^2=b^2+d^2$ and $ab+cd=0$.
- $SU(2)$ adjoint and fundamental transformations
- A finite group G acts freely on a simply connected manifold M
- $SU(3)$ irreps decomposition in subgroup irreps
- Tensors transformations under $so(4)$
Related Questions in TOPOLOGICAL-GROUPS
- Are compact groups acting on Polish spaces essentially Polish?
- Homotopy group of rank 2 of various manifolds
- A question on Group of homeomorphism of $[0,1]$.
- $G\cong G/H\times H$ measurably
- Is a connected component a group?
- How to realize the character group as a Lie/algebraic/topological group?
- Show $\widehat{\mathbb{Z}}$ is isomorphic to $S^1$
- a question on Ellis semigroup
- Pontryagin dual group inherits local compactness
- Property of the additive group of reals
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?