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Topology question: Show that a function f : â„ â†’ â„ is continuous in the Îµ...

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Topology question:
Show that a function f : â„ â†’ â„ is continuous in the Îµ âˆ’ Î´definition of continuity if and only if, for every x âˆˆ â„ and everyopen set U containing f(x), there exists a neighborhood V of x suchthat f(V) âŠ‚ U.

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Topology question: Show that a function f : â„ â†’ â„ is continuous in the Îµ...

60.2K

Verified Solution

Question

Advance Math

Topology question:
Show that a function f : â„ â†’ â„ is continuous in the Îµ âˆ’ Î´definition of continuity if and only if, for every x âˆˆ â„ and everyopen set U containing f(x), there exists a neighborhood V of x suchthat f(V) âŠ‚ U.

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Topology question: Show that a function f : â„ â†’ â„ is continuous in the Îµ...

60.2K

Verified Solution

Question

Advance Math

Topology question:Show that a function f : â„ â†’ â„ is continuous in the Îµ âˆ’ Î´definition of continuity if and only if, for every x âˆˆ â„ and everyopen set U containing f(x), there exists a neighborhood V of x suchthat f(V) âŠ‚ U.

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Topology question: Show that a function f : â„ â†’ â„ is continuous in the Îµ...

Topology question:
Show that a function f : â„ â†’ â„ is continuous in the Îµ âˆ’ Î´definition of continuity if and only if, for every x âˆˆ â„ and everyopen set U containing f(x), there exists a neighborhood V of x suchthat f(V) âŠ‚ U.