# Questions tagged [topological-vector-spaces]

A topological vector space is a vector space $V$ over a topological field $\mathbb{K}$ (typically $\mathbb{K}=\mathbb{R}$ or $\mathbb{K}=\mathbb{C}$), together with a topology on $V$ such that vector addition and scalar multiplication are both continuous. Hilbert spaces and Banach spaces are examples of topological vector spaces.

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### The tensor product of two topological complexes with closed range

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### What's the size of non standard monad for weak topology?

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### Infinite-dimensional affine space in algebraic geometry and algebraic topology

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### Is $C_0(X) $ Frechet-Urysohn with respect to the compact-open topology?

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### $(ST)_{[13]}= S_{[13]}T_{[13]}$ for $S,T \in B(\mathcal{H}\otimes \mathcal{H}).$

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### Is there a topology that makes every basic sequence null?

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### Is a topology sandwiched between two norms compactly generated?

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### Continuous differentiations of functional algebras

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### Is a Banach lattice isomorphic to a Hilbert space in fact a Hilbert lattice?

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### If a subspace $F$ is contained in a subspace $G$, and $H$ is close to $G$, can we choose a subspace of $H$ close to $F$?

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### A “proof” that all separately continuous maps on LF-spaces are continuous

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### Complete topological groups in which all subgroups are closed

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### Topological groups in which all subgroups are closed

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### Is the filtered colimit topology on the space of signed Radon measures linear and locally convex?

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### The Loday-Quillen-Tsygan theorem for topological (Fréchet) algebras

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### Strict topology and $*$-strong toppology on $B(H)$ coincide

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### Is the unit ball of $A \odot B$ strictly dense in that of $M(A \otimes B)$?

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### smooth functions on closed intervals with values in infinite-dimensional spaces

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### Compatibility of inductive and projective limits with dualization in functional analysis

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### Composition mapping for smooth maps with restricted domain

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### Sufficent condition for strict morphism of normed vector spaces

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### Closed image in direct sum

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### Convenient vector space and its locally convex structure

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### Are bounded sets in second duals of locally convex spaces weak* pre-compact?

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### “Weakly” nuclear operators (terminology)

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### Topological constraints on a compact convex set admitting a strictly convex and subdifferentiable real function

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### Can every contractible space be embedded as a convex subset of a vector space?

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### Non-linear weak*-continuous left inverses

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### Weak topology on spaces of measures and Borel sets

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### strong topologies on $C_c^\infty$

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### A question on Grothendieck space

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### Closed convex hull in infinite dimensions vs. continuous convex combinations

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### Equicontinuity-like property of a convex compact set

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### Critical Growth of Dimension for Dense Cover by Linear Subspaces

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### Is the Vietoris topology on compact subsets of $\mathbb R^n$ locally convex?

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### An example of a certain continuous and strictly convex function

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### Bounded weak and weak-$\star$ topologies and metrics

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### Continuity vectors of log-concave measures

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### A set of questions on continuous Gaussian Free Fields (GFF)

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### What is the role of topology on infinite dimensional exterior algebras?

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### Can a quotient space of a locally convex space have finer topology that its domain?

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### Are linear continuous mappings open on totally bounded sets?

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### Reformulation - Construction of thermodynamic limit for GFF

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### Can we say that $f$ admits a $m(X,X^*)$-continuous extension to $X$?

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### If $X$ is separable space then $X^∗$ is separable in all topologies $\tau$ such that $(X^∗,\tau)^∗ =X$?

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### On Köthe sequence spaces

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### Spaces that are comparable with their compacts

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### A complete metric space with some convex-type property

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### Infra-Pták space that is not Pták

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