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Continuity of functions in topology

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#real-analysis #general-topology #continuity
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Are uncountable products of $\mathbb{R}$ always non-sequential?

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#general-topology #set-theory
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Why don't we define neighbourhoods to be open sets?

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#general-topology
521
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Is the unit sphere of $C[0,1]$ connected?

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#general-topology #functional-analysis #normed-spaces #connectedness
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every open set can be expressed as a countable union of compact sets

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#general-topology #compactness
242
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Classification of polynomial knot invariants?

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#general-topology #reference-request #algebraic-topology #knot-theory #knot-invariants
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Homeomorphism preserve compactness and conectedness

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#real-analysis #general-topology #metric-spaces #compactness #connectedness
53
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Showing that a function on a compact metric space X is continuous iff its graph is compact

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#real-analysis #general-topology
53
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$X\neq \varnothing$ topological space that is Compact and Haussdorf without an isolated elements.

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#general-topology #compactness
178
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order topology on singleton set

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#general-topology
64
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Path Contains Two Points Whose Coordinates Differ by Integers

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#real-analysis #general-topology #algebraic-topology #covering-spaces #integer-lattices
429
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Does every quotient map admit a local right inverse?

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#general-topology
999
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Showing a set of matrices is open

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#real-analysis #general-topology #functional-analysis #operator-theory #linear-transformations
7.3k
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Understanding the n-dimensional Simplex in Topology

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#general-topology #graph-theory #simplicial-stuff
108
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When is a subbase a base?

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#general-topology

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