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Is pointwise locally connectedness preserved under a quotient map?

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#general-topology #quotient-spaces #locally-connected
64
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Prove that product of two locally connected spaces is locally connected.

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#general-topology #connectedness #locally-connected
42
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Proof about locally connected

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#general-topology #locally-connected
213
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Does locally compact, locally connected, connected metrizable space admit a metric with connected balls?

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#general-topology #metric-spaces #compactness #connectedness #locally-connected
110
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Definition of local connectedness by Zorich's Mathematical Analysis II

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#general-topology #definition #locally-connected
167
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Metric space that can be written as the finite union of connected subsets but isn't locally connected

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#metric-spaces #compactness #connectedness #continuum-theory #locally-connected
59
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Adding point to connected open set

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#general-topology #connectedness #path-connected #continuum-theory #locally-connected
61
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Is an open connected subspace of $\mathbb{R^2}$ locally path-connected?

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#general-topology #metric-spaces #connectedness #path-connected #locally-connected
39
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Number of components of an open subspace of a compact locally connected space

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#general-topology #compactness #locally-connected
243
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Set of All Points at which $X$ is Locally Connected

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#general-topology #connectedness #locally-connected
124
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Set of Points where X Fails to be Locally Connected

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#general-topology #metric-spaces #compactness #connectedness #locally-connected
102
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Are components of complement of a set $S$ always close to $S$

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#general-topology #examples-counterexamples #connectedness #separation-axioms #locally-connected
39
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Is there a name for local connectedness except you use punctured neigborhoods instead?

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#general-topology #connectedness #locally-connected
213
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The Hahn-Mazurkiewicz Theorem for non-metric spaces

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#general-topology #metric-spaces #examples-counterexamples #locally-connected
327
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The idea of weakly locally connected (connected im kleinen) points, and counterexamples.

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#general-topology #examples-counterexamples #connectedness #locally-connected

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