This book gives a concise exposition of the fundamentals of the theory of topological vector
spaces, complemented by a survey of the most important results of a more subtle nature …

Denote by C _k\mathfrak MC k M the C_k C k-stable closure of the class\mathfrak MM of all
metrizable spaces, ie, C _k\mathfrak MC k M is the smallest class of topological spaces that …

We study the existence of continuous (linear) operators from the Banach spaces\({{\,\textrm
{Lip}\,}} _0 (M)\) of Lipschitz functions on infinite metric spaces M vanishing at a …

Let L (X) be the free locally convex space over a Tychonoff space X. We show that the
following assertions are equivalent:(i) L (X) is ℓ∞-barrelled,(ii) L (X) is ℓ∞-quasibarrelled,(iii) …

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We characterize Ascoli spaces by showing that a Tychonoff space X is Ascoli iff the
canonical map from the free locally convex space L (X) over X into C k (C k (X)) is an …

The paper deals with Ascoli spaces C p (X) and C k (X) over Tychonoff spaces X. The class
of Ascoli spaces X, ie spaces X for which any compact subset K of C k (X) is evenly …

For a compact space K we denote by C w (K)(C p (K)) the space of continuous real-valued
functions on K endowed with the weak (pointwise) topology. In this paper we discuss the …

A family of closed subsets of a topological space $ X $ is called a (strict) $ Cld $-fan in $ X $
if this family is (strictly) compact-finite but not locally finite in $ X $. Applications of (strict) …

A Tychonoff space X is called (sequentially) Ascoli if every compact subset (resp. convergent
sequence) of C k (X) is evenly continuous, where C k (X) denotes the space of all real …