The study of vector space with a topology which makes the maps which sums two vectors and which multiply a vector by a scalar continuous. It's a natural generalization of normed spaces.

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Why This Map is Closed?

Consider the following definition of closed maps, defined in the book Nonlinear Programming by Bazaraa et al.: Let $X$ and $Y$ be nonempty closed sets in $\mathbb{R}^p$ and $\mathbb{R}^q$, ...
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397 views

$\omega$ - space of all sequences with Fréchet metric

I'm working on to prove the following: Show that the convergence in the space $\omega$ (space of all sequences with respect to the Fréchet metric) is the coordinate convergence. Any hint is ...
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When is a notion of convergence induced by a topology?

I'm interested in sufficient conditions for a notion of sequential convergence to be induced by a topology. More precisely: Let $V$ be a vector space over $\mathbb{C}$ endowed with a notion $\tau$ of ...
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299 views

How to define the derivative of Radon measures

Let $M$ be the positive borel measures on a hausdorff topological space $X$, which are finite on compacts sets $--$ i.e. the real cone of radon measures. I am given a definition of a derivative of ...
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682 views

Topology: Proof that a finitely generated cone is closed

Looking for the proof of the lemma asserting that the conical surface (envelope) is a closed space. Thank you.
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142 views

Simple Continuity Question concerning Vector Bundles

I'm a bit confused about the following part in Sir Michael Atiyah's "K-Theory." Let $E = X \times V$ and $F = X\times W$, and let $\phi: E\to F$ be a vector bundle homomorphism. Why is the induced ...
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Finest topology on a space of banach space operators

let $X$ be some Banach space. Let $L(X)$ be the set of continuous operators on $X$ into $X$. Let $(\tau_i)_i$ be a set of topologies on $L(X)$ s.t. $L(X)$ is topological vector space (i.e. addition ...