Existence of basis in some Whitney spaces
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Existence of basis in locally convex spaces has been a hot subject in functional analysis for more than 40 years. We will give some partial solutions to this well-known problem. We will demonstrate two cases of Cantor-type sets with extension property under some special cases. These sets are KN with (DN) where lim sup αn < N and K∞ with (DN) where lim sup αn < ∞.
β and diametral dimension
topological invariants (DN)
power series space of infinite type
nuclear Fr´echet space