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New posts in first-countable
Countable basis and first countable
general-topology
first-countable
A first countable, countably compact space is sequentially compact
general-topology
compactness
first-countable
Second Countable, First Countable, and Separable Spaces
general-topology
separable-spaces
second-countable
first-countable
Constraining a dense sequence on a product space, one factor at a time
general-topology
product-space
second-countable
separable-spaces
first-countable
If $X$ and $Y$ are first countable then $\lim_{x\to x_0}f(x)=y_0$ iff $\lim_{n\to+\infty}f(x_n)=y_0$ for any $x_n\to x_0$
sequences-and-series
general-topology
limits
first-countable
Uncountable Cartesian product of closed interval
general-topology
product-space
first-countable
Topology counterexamples without ordinals
sequences-and-series
general-topology
compactness
second-countable
first-countable
Why is $\mathbb{R}/{\sim}$ not first countable at $[0]$, where $x \sim y \Leftrightarrow x = y\text{ or }x,y \in \mathbb{Z}$?
general-topology
quotient-spaces
first-countable
Mrówka spaces are first-countable
general-topology
compactness
separation-axioms
first-countable
$\prod_{n=1}^{\infty}{\mathbb{R}}$ endowed with the box topology is not first countable.
sequences-and-series
general-topology
convergence-divergence
first-countable
box-topology
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