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Notes on Fréchet spaces

International Journal of Mathematics and Mathematical Sciences, 1999
First, we introduce sequential convergence structures and characterize Fréchet spaces and continuous functions in Fréchet spaces using these structures.
Woo Chorl Hong
doaj   +1 more source

Isometric embedding of a weighted Fermat-Frechet multitree for isoperimetric deformations of the boundary of a simplex to a Frechet multisimplex in the $K$-Space [PDF]

, 2022
In this paper, we study the weighted Fermat-Frechet problem for a $\frac{N (N+1)}{2}-$tuple of positive real numbers determining $N$-simplexes in the $N$ dimensional $K$-Space ($N$-dimensional Euclidean space $\mathbb{R}^{N}$ if $K=0,$ the $N ...
Zachos, Anastasios N.
core   +1 more source

Approximate Identities in Algebras of Compact Operators on Frechet Spaces [PDF]

, 2022
Bounded approximate identity(bai) is a key concept in the theory of amenability of algebras. In this paper, we show that algebra of compact operators on Frechet space X has both theright and left locally bounded approximate identities.
Ayinde, Semiu A.
core   +1 more source

On Fermat-Torricelli Problem in Frechet Spaces

Journal of Nepal Mathematical Society, 2020
We study the Fermat-Torricelli problem (FTP) for Frechet space X, where X is considered as an inverse limit of projective system of Banach spaces. The FTP is defined by using fixed countable collection of continuous seminorms that defines the topology of X as gauges.
G.A. Adebayo, J.A. Oguntuase, S.A. Ayinde, I.A. Osinuga   +3 more
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Frechet Spaces with Nuclear Kothe Quotients [PDF]

Transactions of the American Mathematical Society, 1982
Each separable Frechet non-Banach space X with a continuous norm is shown to have a quotient Y with a continuous norm and a basis. If, in addition, Y can be chosen to be nuclear, we say that X has a nuclear Kothe quotient. We obtain a (slightly technical) characterization of those separable Frechet spaces with nuclear Kothe quotients.
Bellenot, Steven F., Dubinsky, Ed
openaire   +2 more sources

Statistical Bochner Integral on Frechet Space

WSEAS TRANSACTIONS ON MATHEMATICS, 2023
Probability theory including the Bochner integral is a very important part of modern mathematical concepts including the modern theory of probabilities, especially in the concept of mathematical expectation and dispersion. In this, study a statistical approach form of Bochner’s theory is given and extended, but some fundamental properties of ...
Anita Caushi, Ervenila Musta
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I: Fréchet-Urysohn spaces [PDF]

Mathematica Moravica, 2016
In this paper, we introduce the concept ss-sequentially quotient mapping. Using this concept, we characterize s-Fréchet-Urysohn spaces and s-sequential spaces.
Renukadevi V., Prakash B.
doaj  

Spaces whose Pseudocompact Subspaces are Closed Subsets

Applied General Topology, 2004
Every first countable pseudocompact Tychonoff space X has the property that every pseudocompact subspace of X is a closed subset of X (denoted herein by “FCC”).
Alan Dow, Jack R. Porter, R.M. Stephenson, R. Grant Woods   +3 more
doaj   +1 more source

Controllability of mild solutions for fractional neutral evolution equations with state-dependent delay [PDF]

Archives of Control Sciences
This paper examines the controllability of mild solutions for a specific class of neutral fractional evolution equations with finite state-dependent delays in Fréchet space, employing Caputo fractional derivatives.
Selma Baghli-Bendimerad, Chahrazed Boudefla   +1 more
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Tameness in Frechet spaces of analytic functions

, 2016
A Frechet space chi with a sequence {parallel to.parallel to k}(k=1)(infinity) of generating seminorms is called tame if there exists an increasing function sigma : N -> Nsuch that for every continuous linear operator T from chi into itself, there exist ...
Aytuna, Aydin
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