Fréchet property in compact spaces is not preserved by $M$-equivalence

Oleg Okunev

Displaying similar documents to “Fréchet property in compact spaces is not preserved by $M$ -equivalence”

Topological classification of strong duals to nuclear (LF)-spaces

Taras Banakh (2000)

Studia Mathematica

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We show that the strong dual X’ to an infinite-dimensional nuclear (LF)-space is homeomorphic to one of the spaces: $ℝ^{ω}$ , $ℝ^{\infty}$ , $Q \times ℝ^{\infty}$ , $ℝ^{ω} \times ℝ^{\infty}$ , or ${(ℝ^{\infty})}^{ω}$ , where $ℝ^{\infty} = l i m ℝ^{n}$ and $Q = {[- 1, 1]}^{ω}$ . In particular, the Schwartz space D’ of distributions is homeomorphic to ${(ℝ^{\infty})}^{ω}$ . As a by-product of the proof we deduce that each infinite-dimensional locally convex space which is a direct limit of metrizable compacta is homeomorphic either to $ℝ^{\infty}$ or to $Q \times ℝ^{\infty}$ . In particular, the strong dual to any metrizable infinite-dimensional Montel space is homeomorphic...

On AP spaces in concern with compact-like sets and submaximality

Mi Ae Moon, Myung Hyun Cho, Junhui Kim (2011)

Commentationes Mathematicae Universitatis Carolinae

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The definitions of AP and WAP were originated in categorical topology by A. Pultr and A. Tozzi, Equationally closed subframes and representation of quotient spaces, Cahiers Topologie Géom. Différentielle Catég. 34 (1993), no. 3, 167-183. In general, we have the implications: $T_{2} \Rightarrow K C \Rightarrow U S \Rightarrow T_{1}$ , where $K C$ is defined as the property that every compact subset is closed and $U S$ is defined as the property that every convergent sequence has at most one limit. And a space is called submaximal if every dense subset...

Closed universal subspaces of spaces of infinitely differentiable functions

Stéphane Charpentier, Quentin Menet, Augustin Mouze (2014)

Annales de l’institut Fourier

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We exhibit the first examples of Fréchet spaces which contain a closed infinite dimensional subspace of universal series, but no restricted universal series. We consider classical Fréchet spaces of infinitely differentiable functions which do not admit a continuous norm. Furthermore, this leads us to establish some more general results for sequences of operators acting on Fréchet spaces with or without a continuous norm. Additionally, we give a characterization of the existence of a...

On AP and WAP spaces

Angelo Bella, Ivan V. Yashchenko (1999)

Commentationes Mathematicae Universitatis Carolinae

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Several remarks on the properties of approximation by points (AP) and weak approximation by points (WAP) are presented. We look in particular at their behavior in product and at their relationships with radiality, pseudoradiality and related concepts. For instance, relevant facts are: (a) There is in ZFC a product of a countable WAP space with a convergent sequence which fails to be WAP. (b) $C_{p}$ over $σ$ -compact space is AP. Therefore AP does not imply even pseudoradiality in function spaces,...

Displaying similar documents to “Fréchet property in compact spaces is not preserved by M -equivalence”

Topological classification of strong duals to nuclear (LF)-spaces

On AP spaces in concern with compact-like sets and submaximality

Closed universal subspaces of spaces of infinitely differentiable functions

On AP and WAP spaces

Displaying similar documents to “Fréchet property in compact spaces is not preserved by $M$ -equivalence”