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hmw6.2 - X U oo — Y Li oo if and only if f'1[fi is...

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Unformatted text preview: X U oo —} Y Li oo if and only if f'1[fi') is compact for each compact subset K C X. Deduce that if X and Y are homeomorphic, so are X U o-o and F U oo. Find two spaces which are not homeomorphicr yet have homeomorphic one—point compactifications. 5} Show that the unit square is homeomorphic to the equilateral triangle. [Give an explicit formula for the homeomorphism.) Use this to show that you can 'find a curve which completely fills out the unit square. Then explicitly construct a curve which fills out the unit cube. ...
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