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Let Ω be a measure space, and E, F be separable Banach spaces. Given a multifunction $f : Ω \times E \to 2^{F}$ , denote by $N_{f} (x)$ the set of all measurable selections of the multifunction $f (\cdot, x (\cdot)) : Ω \to 2^{F}$ , s ↦ f(s,x(s)), for a function x: Ω → E. First, we obtain new theorems on H-upper/H-lower/lower semicontinuity (without assuming any conditions on the growth of the generating multifunction f(s,u) with respect to u) for the multivalued (Nemytskiĭ) superposition operator $N_{f}$ mapping some open domain G ⊂ X into $2^{Y}$ , where X and Y are Köthe-Bochner...

Semi-continuity and weak-continuity

Takashi Noiri (1981)

Czechoslovak Mathematical Journal

Semicontinuity in $L^{\infty}$ for polyconvex integrals

Emilio Acerbi, Giuseppe Buttazzo, Nicola Fusco (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Viene studiata la semicontinuità rispetto alla topologia di $L^{\infty}(\Omega;\mathbf{R}^{m})$ per alcuni funzionali del Calcolo delle Variazioni dipendenti da funzioni a valori vettoriali.

Semicontinuity of maps which are limits of sequences of Baire continuous multivalued maps

M. Matejdes (1990)

Matematički Vesnik

Semicontinuity of maps which are limits of sequences of quasi-continuous maltivalued maps

J. Ewert (1987)

Matematički Vesnik

Semi-continuity of set-valued monotone mappings

P. Kenderov (1975)

Fundamenta Mathematicae

Semicontinuous integrands as jointly measurable maps

Oriol Carbonell-Nicolau (2014)

Commentationes Mathematicae Universitatis Carolinae

Suppose that $(X, 𝒜)$ is a measurable space and $Y$ is a metrizable, Souslin space. Let $𝒜^{u}$ denote the universal completion of $𝒜$ . For $x \in X$ , let $\underset{̲}{f} (x, \cdot)$ be the lower semicontinuous hull of $f (x, \cdot)$ . If $f : X \times Y \to \bar{ℝ}$ is $(𝒜^{u} \otimes ℬ (Y), ℬ (\bar{ℝ}))$ -measurable, then $\underset{̲}{f}$ is $(𝒜^{u} \otimes ℬ (Y), ℬ (\bar{ℝ}))$ -measurable.

Semi-generalized continuous maps in topological spaces.

Caldas Cueva, Miguel (1995)

Portugaliae Mathematica

Semilocal connectedness of product spaces and $s$ -continuity of maps.

Ewert, Janina (2000)

International Journal of Mathematics and Mathematical Sciences

Semi-open sets in biclosure spaces

Jeeranunt Khampakdee, Chawalit Boonpok (2009)

Discussiones Mathematicae - General Algebra and Applications

The aim of this paper is to introduce and study semi-open sets in biclosure spaces. We define semi-continuous maps and semi-irresolute maps and investigate their behavior. Moreover, we introduce pre-semi-open maps in biclosure spaces and study some of their properties.

Semi-precontinuous functions and properties of generalized semi-preclosed sets in topological spaces.

Navalagi, G.B. (2002)

International Journal of Mathematics and Mathematical Sciences

Semi-quotient mappings and spaces

Moiz ud Din Khan, Rafaqat Noreen, Muhammad Siddique Bosan (2016)

Open Mathematics

In this paper, we continue the study of s-topological and irresolute-topological groups. We define semi-quotient mappings which are stronger than semi-continuous mappings, and then consider semi-quotient spaces and groups. It is proved that for some classes of irresolute-topological groups (G, *, τ) the semi-quotient space G/H is regular. Semi-isomorphisms of s-topological groups are also discussed.

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Semi-closed sets and the associated topology

Semi-confluent and weakly confluent images of tree-like and atriodic continua

Semi-confluent mappings.

Semi-confluent mappings and their invariants

Semicontinuity and continuous selections for the multivalued superposition operator without assuming growth-type conditions