Descriptive topology for analysts

JC Ferrando - Revista de la Real Academia de Ciencias Exactas …, 2020‏ - Springer
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[HTML][HTML] On the Ascoli property for locally convex spaces

S Gabriyelyan - Topology and its Applications, 2017‏ - Elsevier
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 …

[HTML][HTML] The Ascoli property for function spaces

S Gabriyelyan, J Grebík, J Kakol, L Zdomskyy - Topology and its …, 2016‏ - Elsevier
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 …

Ascoli's theorem for pseudocompact spaces

S Gabriyelyan - Revista de la Real Academia de Ciencias Exactas …, 2020‏ - Springer
A Tychonoff space X is called (sequentially) Ascoli if every compact subset (resp. convergent
sequence) of C_k (X) C k (X) is equicontinuous, where C_k (X) C k (X) denotes the space of …

Topological properties of strict (LF)-spaces and strong duals of Montel strict (LF)-spaces

S Gabriyelyan - Monatshefte für Mathematik, 2019‏ - Springer
Abstract Following Banakh and Gabriyelyan (Monatshefte Math 180: 39–64, 2016), a
Tychonoff space X is Ascoli if every compact subset of C_k (X) C k (X) is equicontinuous. By …