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A continuous function $g: \mathbb{R}^n \rightarrow \mathbb{R}^m$, with $m > n$,

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#general-topology
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A relatively open subset of $\partial \Omega$ with a relative boundary.

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#general-topology #differential-topology
134
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Is countable base basis for topology

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#general-topology
120
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Open set in terms of nets

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#general-topology #examples-counterexamples #nets
476
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Showing that two quotient spaces are homeomorphic

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#general-topology
91
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Continuity of a function (upper envelope)

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#real-analysis #general-topology #continuity #normed-spaces
328
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Is the Hairy Ball Theorem equivalent to saying that the Hopf Fibration has no global sections?

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#general-topology #algebraic-topology #differential-topology #fiber-bundles #hopf-fibration
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Why is $(0, \infty)$ an open set and $ [0, \infty)$ a closed set?

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#general-topology
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Why are these not manifolds?

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#general-topology #manifolds
195
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Topological spaces and open sets

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#general-topology
33
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Topological Spaces and closed sets

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#general-topology #proof-verification
160
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Co-finite Topologies

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#general-topology
166
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How to prove Baire Category theorem by Zorn's lemma?

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#general-topology #axiom-of-choice #baire-category
98
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Is it true that $X $ is complete iff $Y$ is complete.

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#real-analysis #general-topology
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Is it true that $\varinjlim\left( A_{i}\times B\right)\cong \left(\varinjlim A_{i}\right)\times B$ in topological spaces?

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#general-topology #continuity

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