Everything involving general topological spaces: generation and description of topologies; open and closed sets, neighborhoods; interior, closure; connectedness; compactness; separation axioms; bases; convergence: sequences, nets and filters; continuous functions; compactifications; function spaces; ...

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interior of convex hull relatively open

Consider $k+1$ affinely independent vectors $\left\{p_0,p_1, \dots, p_k \right \}$ in $n$-dimensional euclidean vector space $n>k$ and consider their convex hull. It is known that each point $x$ of ...
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Why this set is dense in $C_0(\mathbb{R})$

Let $C_0=\{f~|~ f:\mathbb{R}\to\mathbb{R},f~is~continous,\lim\limits_{\vert x\vert \to\infty}f(x)=0\}$ $A=\{f~|~f(x)=p(x)e^{-x^2},p(x)~is~polynomials\}$ Why $A$ is dense in $C_0$. The topology ...
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Is this property of continuous functions equivalent to anything familiar? If not, does it at least have a name?

If I understand correctly, every morphism of topological spaces $f : Y \leftarrow X$ factorizes uniquely into a composite of three morphisms $$f = c \circ b \circ a$$ such that $c : Y \leftarrow ...