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Results tagged with gn.general-topology
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user 477203
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
1
vote
1
answer
106
views
Conditions that ensure the metric topology of $E$ coincides with the initial topology induce...
Let $(E, d)$ be a metric space and $\mathcal F$ a collection of real-valued functions on $E$. Assume that for all $x,x_n \in E$ with $n\in \mathbb N$,
$$
x_n \to x \iff [f(x_n) \to f(x) \quad \forall …
- 657
1
vote
0
answers
62
views
Is $L^p_\text{loc} (Y)$ dense in $(L^0(Y), \hat \rho)$?
Below we use Bochner measurability and Bochner integral. Let
$(Y, d)$ be a separable metric space,
$\mathcal B$ Borel $\sigma$-algebra of $Y$,
$\nu$ a $\sigma$-finite Borel measure on $Y$,
$(Y, \over …
- 657