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Union and intersection of $F_\sigma$ sets

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#general-topology #analysis
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Question about the definition of a topological space

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#general-topology #definition
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Why, in topology, is continuity defined with inverse images?

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#general-topology
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when is the separation $T_2$ axiom needed

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#general-topology
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Understanding the inverse limit and universal property of topological spaces

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#general-topology #category-theory #proof-explanation #limits-colimits #universal-property
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If $E$ is a locally compact separable metric space, then $E$ is the union of a sequence of compact

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#general-topology
425
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Locally compact Hausdorff then Tychonoff

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#general-topology #separation-axioms
231
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Doubt in understanding proof in Topology by Munkres Proof 20.5

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#general-topology #metric-spaces #proof-explanation
51
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general topology on set of neighbourhoods

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#general-topology
340
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Fundamental group of uncountable space with cofinite topology

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#general-topology #algebraic-topology #fundamental-groups
134
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Example of a nowhere dense set

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#real-analysis #general-topology #metric-spaces
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Every ray from a point in the interior of a compact convex set intersects with its boundary.

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#general-topology #euclidean-geometry
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Is a dense set always infinite?

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#real-analysis #general-topology
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Is a connected set always an uncountably infinite set?

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#real-analysis #general-topology #connectedness
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Domain of a piecewise continuous function

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#real-analysis #calculus #general-topology #functions #fourier-series

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