Let be p:G to G/N a quotient map.Is it open?
Let be f:G to H an open map. Is it quotient map?
Here G and H are topological groups, and N is an subgroup.
Topological Groups and Quotient and Open Maps are investigated.
Topological Space : Subspace - 19. Let X be a topological space and let Y be a subset of X. Check that the so-called subspace topology is indeed a topology of Y.
(question is also included in attachment)
Functional analysis proof -
Just a note on notation: X*_w* is X* (set of all linear functionals) with a weak-* topology (the weakest topology in which all functionals are continuous)
This posting is for #1
See attached
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Topological Space : Subspace - Let X be a topological space and let Y be a subset of X. Check that the so-called subspace topology is indeed a topology on Y.
Topology : Subspace - Suppose (X,T) is a topological space. Let Y be non-empty subset of X. The the set J={intersection(Y,U) : U is in T} is called the subspace toplogy on Y. Prove that J indeed a toplogy on Y i.e., (Y, ...
Topological Spaces and Continuity - Please see the attached file for the fully formatted problems.
Let be a real valued function on a topological space .
Show that is continuous if and only if for each real number the set ...