New posts in general-topology

Verifying continuity of the deformation retraction of the mapping cylinder

general-topology algebraic-topology continuity

Separation in compact spaces

real-analysis general-topology proof-verification continuity

Continuously extending a set of independent vectors to a basis.

linear-algebra general-topology continuity

Characterization of compactness in weak* topology

general-topology functional-analysis compactness

$\sigma$-algebra of sets that are both $G_\delta$ and $F_\sigma$

real-analysis general-topology probability-theory measure-theory

What are some interesting counterexamples given by finite topological spaces?

general-topology examples-counterexamples

Continuous Deformation Of Punctured Torus

general-topology algebraic-topology

Topological Open Mapping Theorem for mappings between different Euclidean dimensions?

general-topology analysis multivariable-calculus reference-request differential-topology

How many ultrafilters there are in an infinite space?

general-topology proof-explanation cardinals filters

Properties of space $X = T \cup \bigcup_{n=1}^{\infty} S_n \cup \{ (0,q) : q \in \mathbb Q \wedge q \in [0,1] \} $

general-topology connectedness locally-connected

Brouwer's fixed point theorem and the one-point topology

general-topology logic category-theory fixed-point-theorems

If $f_{n}$ has a dense image, then $\bigcap (f_{1}\circ\cdots\circ f_{n})(X_{n})$ is dense

general-topology the-baire-space

Connectedness of sets in the plane with rational coordinates and at least one irrational

general-topology

Homotopy extension property vs. good pairs

general-topology algebraic-topology

Why the weak topology is never metrizable?

general-topology functional-analysis metric-spaces

Is total boundedness a topological property?

general-topology metric-spaces examples-counterexamples

$\{(x,y)\!\in\!\mathbb{B}^n; -\varepsilon\leq-\|x\|^2\!+\!\|y\|^2\leq\varepsilon\}\approx\mathbb{B}^k\!\times\!\mathbb{B}^{n-k}$

general-topology algebraic-topology differential-geometry differential-topology geometric-topology

A question on a compact space [closed]

general-topology compactness

Is this a sufficient condition for two spaces to be homeomorphic; proof or counter example please.

general-topology

Find a point $l$ in the closure of $A$ so that no sequence with values in $A$ converges to $l$.

general-topology