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Let $X$ be a compact Hausdorff space with a point $x$ such that $X ∖ {x}$ is linearly Lindelöf. Is then $X$ first countable at $x$ ? What if this is true for every $x$ in $X$ ? We consider these and some related questions, and obtain partial answers; in particular, we prove that the answer to the second question is “yes” when $X$ is, in addition, $ω$ -monolithic. We also prove that if $X$ is compact, Hausdorff, and $X ∖ {x}$ is strongly discretely Lindelöf, for every $x$ in $X$ , then $X$ is first countable. An example of linearly Lindelöf...

Convergence in exponentiable spaces.

Pisani, Claudio (1999)

Theory and Applications of Categories [electronic only]

Convergence in fuzzy topological spaces

Lowen, R. (1977)

General topology and its relations to modern analysis and algebra IV

Convergence in Relational Structures.

W. TAYLOR (1970)

Mathematische Annalen

Convergence of a sequence of fixed points in a uniform space

S. P. Acharya (1976)

Matematički Vesnik

Convergence of a sequence of sets in a Hadamard space and the shrinking projection method for a real Hilbert ball.

Kimura, Yasunori (2010)

Abstract and Applied Analysis

Convergence of conditional expectations for unbounded closed convex random sets

Charles Castaing, Fatima Ezzaki, Christian Hess (1997)

Studia Mathematica

We discuss here several types of convergence of conditional expectations for unbounded closed convex random sets of the form $E^{ℬ_{n}} X_{n}$ where $(ℬ_{n})$ is a decreasing sequence of sub-σ-algebras and $(X_{n})$ is a sequence of closed convex random sets in a separable Banach space.

Convergence of convex functions and generalized inf-convolutive approximations. (Convergences des fonctions convexes et approximations inf-convolutives généralisées.)

Mentagui, D., El Hajioui, K. (2002)

Publications de l'Institut Mathématique. Nouvelle Série

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