New posts in Metric Spaces

Continuous function between a lower semi-continuous function and an upper semi-continuous function.

If a sequence $\{x_{n}\}$ is a Cauchy sequence and the sequence has a limit point $x_{0}$ then $x_{n} \rightarrow x_{0}$

Can I get a sequence of bounded functions converging pointwise to $f(x)=1/x$ for $x$ non zero and $0$ for $x$ zero?

If $K$ is compact and $(f_k)\subseteq C(K)$ is dense, then $x_n\to x$ in $K$ iff $f_k(x_n)\to f_k(x)$ for each $k$

Topological spaces which are not pseudometrizable.

Proof that the inverse image of a single element is a discrete space

Is $x \mapsto d(x, A)$ a quotient map?

Can a Cauchy sequence converge for one metric while not converging for another?

Does $d(x,y) = \log(1 + | x - y |)$ define a metric on $\mathbb{R}$?

Isometry and compactness.