# 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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### Extension of Vector Field in the $\mathcal{C}^r$ topology

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### Is a set of nuclear functionals equicontinuous in compact-open topology if it is equicontinuous on each compact set?

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### Two notions of boundedness in metrizable topological vector space [closed]

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### Is each cometrizable space a subspace of a cometrizable topological group?

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### Spectral theory without topology

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### Invariant compact in division ring

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### Mackey topology characterising property

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### Openness of invertibility in Fréchet spaces for families parameterized by compact spaces

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### Compactness if Emery (semi-martingale) topology

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### Gelfand-Pettis integral: what does it mean for a topological vector space to “admit a dual space?”

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### Is the compact-open topology on the dual of a separable Frechet space sequential?

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### The completeness of spaces of continuous functions with the compact-open topology

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### On convergent sequences in locally convex topological vector spaces

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### References on categorical TVS theory

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### Is restriction a closed map?

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### Compactness of operators and norming sets

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### Smooth functions with values in bornological vector space

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### Is each closed subgroups of $\mathbb R^\omega$ isomorphic to a Tychonoff product of locally compact Abelian groups?

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### Approximation of the identity by finite range functions in topological vector spaces

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### Are second-countable subsets of topological vector spaces metrizable?

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### Boundedness of Dirac deltas

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### Separable Lindelöf locally convex spaces that are not second-countable

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### Closure in the strong dual topology

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### Measurability of the product on particular topological vector spaces

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### On sections into Banach bundles over a compact manifold

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### Topological vector space textbook with enough applications

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### Countable dense subset of functions of exponential type 1 that decay along the positive real axis

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### Bilinear product of two summable families

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### Recognizing locally convex spaces on which all bounded linear functionals are continuous

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### When is the strict topology bornological?

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### Closed vector subspaces of large powers of R

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### Bohr compactification as a topological compactification

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### An equivalent condition for second countable locally convex spaces

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### Can a topological vector space be probabilistic metric space too? [closed]

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### References on topological rings

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### Criterion of reflexivity 2

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### When are the closed convex subsets countable intersections of halfspaces

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### Criterion of reflexivity

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### Is any dual metrizable locally convex space a Frechet space?

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### Topologies of pairs and closed bounded convex sets

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### Criterion for weak compactness

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### A criterion for norming sets

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### Well definition of a function

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### Fixed point of a group action

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### Semi-embeddings and weak compactness

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### Why is an inductive limit of bornological spaces bornological?

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### Proof of the Schauder Lemma

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### DF-algebras and DF-modules

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### Topology of the Hamel basis in a TVS

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