$$\omega ^\omega $$-Base and infinite-dimensional compact sets in locally convex spaces

$T^\omega$-representations of compact sets

We explore representing the compact subsets of a given represented space by infinite sequences over Plotkin's T. We show that compact Hausdorff spaces with a proper dyadic subbase admit representations of their compact subsets in such a way that compact sets are essentially underspecified points. We can even ensure that a name of an n-element compact set contains at most n occurrences of ⊥.

Approximate Convexity and Submonotonicity in Locally Convex Spaces

RESTRICTED p-CENTERS FOR SETS IN REAL LOCALLY CONVEX SPACES

Let X ,Z be a pair of real linear spaces put in duality by a separating bilinear form 〈, 〉, and endowed with compatible locally convex topologies respectively. A subset F of X is said to be p-bounded if sup p(x) : x ∈ F < ∞. We denote the collection of all nonempty p-bounded subsets of X by p(X ). Given x ∈ X , F ∈ p(X ), and V ⊆ X , write rp(F ; x) = sup p(y − x) : y ∈ F , radp(F ;V ) = inf rp...

BASE AXIOMS AND SUBBASE AXIOMS IN M-FUZZIFYING CONVEX SPACES

Based on a completely distributive lattice $M$, base axioms and subbase axioms are introduced in $M$-fuzzifying convex spaces. It is shown that a mapping $mathscr{B}$ (resp. $varphi$) with the base axioms (resp. subbase axioms) can induce a unique $M$-fuzzifying convex structure with  $mathscr{B}$ (resp. $varphi$) as its base (resp. subbase). As applications, it is proved that bases and subbase...

Smooth negligibility of compact sets in infinite-dimensional Banach spaces, with applications