general topology | Math Help

Prove that there exists a unique topology $T$ for which $ P $ is its subbasis and that topological space $ ( T, \mathbb{N ^{*}})$ is metrisable .

general-topology
Updated April 21, 2019 14:20 PM

If $U$ and $V$ are disjoint , prove that $ \operatorname{Int} (\operatorname{Cl}U) $ and $\operatorname{Int}(\operatorname{Cl}(V) $ are disjoint sets.

general-topology
Updated April 21, 2019 11:20 AM

Prove that topological space $ \mathbb{R^2} $ with dictionary order topology is first countable, but not second countable.

general-topology
Updated April 21, 2019 09:20 AM

Check on a proof I saw on another thread: Metrizable Lindelof spaces have a countable basis

general-topology proof-verification
Updated April 21, 2019 08:20 AM

Inscribed Rectangle Proof (Basic Question)

general-topology curves
Updated April 21, 2019 08:20 AM

How to find an embedded submanifold in $\mathbb{R}^{n}$ which pass through some given points in $\mathbb{R}^{n}$ and has the lowest dimension?

differential-geometry riemannian-geometry low-dimensional-topology
Updated April 21, 2019 08:20 AM

Let $X$ be a topological space and $U$ be aproper dense open subset of $X$. Pick the correct statement from the following

general-topology
Updated April 21, 2019 07:20 AM

Problem about real projective plane.

general-topology proof-verification
Updated April 21, 2019 07:20 AM

Show that $\{x \in X: \|f(x) \|+... +\| f^{(p)}(x) \| \geq \varepsilon\}$ is compact

general-topology derivatives compactness
Updated April 21, 2019 07:20 AM

For continuously differentiable $f,$ is it true that the set $\{(x_0,x_1)\in (0,1)^2: |f(x_0)| + |f'(x_1)| \geq \epsilon\}$ not compact in $(0,1)^2?$

real-analysis general-topology functional-analysis derivatives continuity
Updated April 21, 2019 06:20 AM

Property of closed balls and closed sets

general-topology metric-spaces
Updated April 21, 2019 05:20 AM

Polynomial ring a module over ring of invariants

computer-algebra-systems invariant-theory computational-algebra general-linear-group
Updated April 21, 2019 05:20 AM

Covering dimension of boundary of compact subset of $\mathbb{R}^n$

general-topology manifolds dimension-theory hausdorff-dimension
Updated April 21, 2019 05:20 AM

Understanding a mapping cylinder.

general-topology algebraic-topology
Updated April 21, 2019 04:20 AM

General Point set Topology: The Closure of a set is Closed

general-topology proof-explanation
Updated April 21, 2019 02:20 AM

Closed graph and fixed points

general-topology functional-analysis fixed-point-theorems fixedpoints
Updated April 21, 2019 02:20 AM

Fundamental group of the complement of $3$ disjoint hypersurfaces in $\mathbb{C}P^2$

algebraic-topology projective-space fundamental-groups
Updated April 21, 2019 01:20 AM

Fundamental group Pi1(SU(n)) and Pi2(SU(n))

general-topology algebraic-topology fundamental-groups
Updated April 21, 2019 00:20 AM

Free product with amalgamation vs pushout

group-theory algebraic-topology free-product
Updated April 20, 2019 20:20 PM

Let $X$ be a topological space and $A \subset X$ a subset of $X$. Is $ Fr (Int A ) = Fr(A)$?

general-topology
Updated April 20, 2019 19:20 PM

general topology : Math Help