2-sphere intrinsic definition by gluing disks' boundaries
Aug 6, 2025 · Basically one starts assigning each disk the subspace topology from R 2 and then taking the quotient topology obtained by gluing their boundaries. Starting from the above …
The wrong turn of string theory: our world is SUSY at low energies
Nov 17, 2020 · However, we can sidestep the necessity for compactification by postulating that spacetime is a subspace of a multidimensional configuration space—specifically, the space of …
Finding Basis for Subspaces of R4 - Physics Forums
Jan 29, 2009 · Formulation of a proof of subspaces Jan 22, 2019 Replies 10 Views 2K T is cyclic iff there are finitely many T-invariant subspace Oct 20, 2018 Replies 4 Views 3K Linear …
Understanding Subspace Basis and Counterexample - Physics …
Feb 8, 2010 · If W is a subspace of V and we are given a basis for W, then we can extend that to a basis for V. That is, the basis for V will consist of all vectors in the basis for W together with …
Orthogonal Projection Onto a Subspace? - Physics Forums
Aug 23, 2010 · What he has calculated is the "shadow" of w on the subspace which is what he apparently meant by the orthogonal projection onto the subspace. What I suggested to you …
Determining if a set is a subspace. • Physics Forums
Oct 5, 2014 · I am trying to determine how to tell if a set is a subspace. The problem reads like this: Determine if the described set is a subspace. If so, give a proof. If not, explain why not. …
Show that a "cross" is not a topological manifold • Physics Forums
Jul 30, 2024 · Hi, I've a doubt about the following example in "Introduction to Manifold" by L. Tu. My understanding is that if one assumes the subspace topology from ##\\mathbb R^2## for …
Why Does a Subset of a Vector Space Need the Zero Vector to Be …
Feb 7, 2008 · If each subspace has its own zero vector, then combine these subspaces in order to get a bigger subspace or even the whole space. We will get bunch of different zeros and the …
What is a Closed Linear Subspace? - Physics Forums
Jun 10, 2011 · A closed linear subspace is defined as a subspace in a Hilbert space where any convergent sequence of vectors within that subspace converges to a limit that is also within …
Prove that the intersection of subspaces is subspace
Jul 8, 2009 · The discussion revolves around proving that the intersection of any collection of subspaces of a vector space V is itself a subspace of V. Participants clarify that the …