New posts in General Topology

Why does the definition of topological space require that the empty set be open?

Confusion on why 2 equivalence classes are either equal or disjoint

Why do we care about the Hilbert Cube?

Examples of almost compact spaces.

Existence of a path between two sides of a square, which is contained in the intersection of two open subsets of it

The subspace $C$ of the space $(X,d)$ is compact

For any $S \subseteq \mathbf{R}$, if $\partial S$ denotes the boundary of $S$, prove that $\partial(\partial S) \subseteq \partial S$.

What is an open set in a topological space?

Is completeness over a normed space invariant under linear homeomorphisms?

In ZF, does the ring of continuous functions $C([0,1], \mathbb{R})$ have prime ideals which is not maximal?