Stability of closedness of closed convex sets under linear mappings

Publication date: 22 January 2020

Abstract: We study the problem of when the continuous linear image of a fixed closed convex set

X s u b s e t m a t h b b R^{n}

is closed. Specifically, we improve the main results in the papers cite{Borwein2009, Borwein2010} by showing that for all, except for at most a

s i g m a

-porous set, of the linear mappings

T

from

m a t h b b R^{n}

into

m a t h b b R^{m},

not only

T (X)

is closed, but there is also an open neighborhood of

T

whose members also preserve the closedness of

X .

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