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Show that each connected component of a topological space $X$ is connected.

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#general-topology #proof-verification #proof-writing
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Compact spaces that depend on choice?

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#general-topology #set-theory #compactness #axiom-of-choice
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Intersection of Compact Sets Is Not Compact

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#general-topology
140
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Connected components and diffeomorphism

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#real-analysis #general-topology #analysis
101
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Second countable profinite topological space any equivalence class is a finite union of basic open sets

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#general-topology #elementary-set-theory
56
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Edit: Prove that $(U,\delta)$ is complete where $\delta(x,y)=d(x,y)+\Big|\frac{1}{d(x,F)}-\frac{1}{d(y,F)}\Big|,\;\;\forall\; x,y\in U$

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#general-topology #metric-spaces #topological-vector-spaces
428
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$E$ be a normed vector space. Prove that $U+V$ is open in E

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#general-topology #metric-spaces #topological-vector-spaces
75
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If $d_1\sim d_2$ and $I:(E,d_1)\to(E,d_2) $, prove that $I$ is continuous.

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#general-topology #metric-spaces #topological-vector-spaces
119
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What is the order type of the set of smooth functions ordered by growth rate?

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#real-analysis #general-topology #order-theory #ordinals #well-orders
422
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Finite Unions of Dendrites

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#general-topology #plane-curves #plane-geometry #infinite-graphs #continuum-theory
124
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Why a map which is close to the identity on the boundary of a disk has a zero?

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#general-topology #algebraic-topology #fixed-point-theorems
108
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Weaker condition for path independence of $\int_{\gamma } f$ on disconnected open subset

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#general-topology #complex-analysis #multivariable-calculus #derivatives #complex-integration
66
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PDE Compact set

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#general-topology #partial-differential-equations
180
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composition of fiber bundles

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#general-topology #algebraic-topology
741
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How to prove fat Cantor set has no isolated point

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#general-topology #cantor-set

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