query: If $T$ is a linear functional then $T$ is an open map
positive_passages.docid: 78344
positive_passages.text: Nonconstant linear functional on a topological vector space is an open mapping
negative_passages.docid: 88311
negative_passages.text: Linear functional f(v)=0 imply v=0
negative_passages.docid: 28731
negative_passages.text: Banach space in functional analysis
negative_passages.docid: 101467
negative_passages.text: Let $T:V\to V$ be a linear map, where $V$ is an inner product space. Given $T^2=\frac{T+T^*}{2}$, prove that $T$ is normal and that $T=T^2$.
negative_passages.docid: 142740
negative_passages.text: If $\varphi \in E'$ and $A$ is convex and open then $\varphi (A)$ is an open interval
negative_passages.docid: 140212
negative_passages.text: Prove that there exists a unique linear map that extends the map from a basis
negative_passages.docid: 38033
negative_passages.text: A surjective linear map into a finite dimensional space is open
negative_passages.docid: 59424
negative_passages.text: Showing that $B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$ is an open set
negative_passages.docid: 52388
negative_passages.text: The equivalence of open-set definition of continuous mappings to the $\epsilon-\delta$ definition
negative_passages.docid: 68724
negative_passages.text: $||T-I|| < 1$ implies that $T$ is invertible.
negative_passages.docid: 114458
negative_passages.text: $f$ is entire and maps a rectangle to a rectangle, then $f$ is linear
negative_passages.docid: 60692
negative_passages.text: Is this map to a finite dimensional topological vector space an open map?
negative_passages.docid: 62887
negative_passages.text: Proof that a linear transformation is continuous
negative_passages.docid: 53528
negative_passages.text: If $\ker f\subset \ker g$ where $f,g $ are non-zero linear functionals then show that $f=cg$ for some $c\in F$.
negative_passages.docid: 127900
negative_passages.text: Interior of closure of open set in topological space
negative_passages.docid: 133266
negative_passages.text: If $(X, \mathcal{T})$ has a countable subbasis, then it has a countable basis
negative_passages.docid: 109046
negative_passages.text: Is the complement of an open ball in a Banach space connected?