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Michael's selection theorem
reverse-reverse of Michael selection theoremLeray-Schauder fixed point theoremSegment ordered density conjecture.Clarification on the difference between Brouwer Fixed Point Theorem and Schauder Fixed point theoremCorollary of Tietze extension theoremWeak * lower semicontinuityHahn-Banach theorem geometric form complex caseHow to prove Hahn-Banach separation theorem for $X^*times mathbbR$ version?Strong separation theorem in dual spaceHow close is Mazur's Separation Theorem and the 2nd geometric form of HBT?
$begingroup$
Michael's selection theorem states that a lower hemicontinuous multivalued map with nonempty convex closed values $displaystyle Fcolon Xrightrightarrows E$ from a paracompact space $X$ to a Banach space $E$ admits a continuous selection.
If we replace the assumption "lower hemicontinuous multivalued map with nonempty convex closed values" by one of the following assumptions, does the theorem still hold?
- "hemicontinuous multivalued map with nonempty closed values".
- "lower hemicontinuous multivalued map with nonempty connected closed values".
general-topology functional-analysis multivalued-functions
asked Mar 22 at 9:26
DinoDino
1216
$endgroup$
add a comment |
$begingroup$
Michael's selection theorem states that a lower hemicontinuous multivalued map with nonempty convex closed values $displaystyle Fcolon Xrightrightarrows E$ from a paracompact space $X$ to a Banach space $E$ admits a continuous selection.
If we replace the assumption "lower hemicontinuous multivalued map with nonempty convex closed values" by one of the following assumptions, does the theorem still hold?
- "hemicontinuous multivalued map with nonempty closed values".
- "lower hemicontinuous multivalued map with nonempty connected closed values".
general-topology functional-analysis multivalued-functions
asked Mar 22 at 9:26
DinoDino
1216
$endgroup$
add a comment |
$begingroup$
Michael's selection theorem states that a lower hemicontinuous multivalued map with nonempty convex closed values $displaystyle Fcolon Xrightrightarrows E$ from a paracompact space $X$ to a Banach space $E$ admits a continuous selection.
If we replace the assumption "lower hemicontinuous multivalued map with nonempty convex closed values" by one of the following assumptions, does the theorem still hold?
- "hemicontinuous multivalued map with nonempty closed values".
- "lower hemicontinuous multivalued map with nonempty connected closed values".
general-topology functional-analysis multivalued-functions
asked Mar 22 at 9:26
DinoDino
1216
$endgroup$
Michael's selection theorem states that a lower hemicontinuous multivalued map with nonempty convex closed values $displaystyle Fcolon Xrightrightarrows E$ from a paracompact space $X$ to a Banach space $E$ admits a continuous selection.
If we replace the assumption "lower hemicontinuous multivalued map with nonempty convex closed values" by one of the following assumptions, does the theorem still hold?
- "hemicontinuous multivalued map with nonempty closed values".
- "lower hemicontinuous multivalued map with nonempty connected closed values".
general-topology functional-analysis multivalued-functions
general-topology functional-analysis multivalued-functions
asked Mar 22 at 9:26
DinoDino
1216
asked Mar 22 at 9:26
DinoDino
1216
asked Mar 22 at 9:26
DinoDino
1216
asked Mar 22 at 9:26
DinoDino
1216
asked Mar 22 at 9:26
DinoDino
1216
1216
add a comment |
add a comment |
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