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Closure-preserving covers in function spaces

David Guerrero Sánchez (2010)

Commentationes Mathematicae Universitatis Carolinae

It is shown that if C p ( X ) admits a closure-preserving cover by closed σ -compact sets then X is finite. If X is compact and C p ( X ) has a closure-preserving cover by separable subspaces then X is metrizable. We also prove that if C p ( X , [ 0 , 1 ] ) has a closure-preserving cover by compact sets, then X is discrete.

CM-Selectors for pairs of oppositely semicontinuous multivalued maps with p -decomposable values

Hôǹg Thái Nguyêñ, Maciej Juniewicz, Jolanta Ziemińska (2001)

Studia Mathematica

We present a new continuous selection theorem, which unifies in some sense two well known selection theorems; namely we prove that if F is an H-upper semicontinuous multivalued map on a separable metric space X, G is a lower semicontinuous multivalued map on X, both F and G take nonconvex L p ( T , E ) -decomposable closed values, the measure space T with a σ-finite measure μ is nonatomic, 1 ≤ p < ∞, L p ( T , E ) is the Bochner-Lebesgue space of functions defined on T with values in a Banach space E, F(x) ∩ G(x) ≠ ∅...

Coarse dimensions and partitions of unity.

N. Brodskiy, J. Dydak (2008)

RACSAM

Gromov and Dranishnikov introduced asymptotic and coarse dimensions of proper metric spaces via quite different ways. We define coarse and asymptotic dimension of all metric spaces in a unified manner and we investigate relationships between them generalizing results of Dranishnikov and Dranishnikov-Keesling-Uspienskij.

Coincidence and fixed point theorems for nonlinear hybrid generalized contractions

H. K. Pathak, Shin Min Kang, Yeol Je Cho (1998)

Czechoslovak Mathematical Journal

In this paper we first prove some coincidence and fixed point theorems for nonlinear hybrid generalized contractions on metric spaces. Secondly, using the concept of an asymptotically regular sequence, we give some fixed point theorems for Kannan type multi-valued mappings on metric spaces. Our main results improve and extend several known results proved by other authors.

Coincidence point theorems in certain topological spaces

Jong Soo Jung, Yeol Je Cho, Shin Min Kang, Yong Kab Choi, Byung Soo Lee (1999)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we establish some new versions of coincidence point theorems for single-valued and multi-valued mappings in F-type topological space. As applications, we utilize our main theorems to prove coincidence point theorems and fixed point theorems for single-valued and multi-valued mappings in fuzzy metric spaces and probabilistic metric spaces.

Colorings of Periodic Homeomorphisms

Yuji Akaike, Naotsugu Chinen, Kazuo Tomoyasu (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

We calculate the exact value of the color number of a periodic homeomorphism without fixed points on a finite connected graph.

Comaximal graph of C ( X )

Mehdi Badie (2016)

Commentationes Mathematicae Universitatis Carolinae

In this article we study the comaximal graph Γ 2 ' C ( X ) of the ring C ( X ) . We have tried to associate the graph properties of Γ 2 ' C ( X ) , the ring properties of C ( X ) and the topological properties of X . Radius, girth, dominating number and clique number of the Γ 2 ' C ( X ) are investigated. We have shown that 2 ≤ Rad Γ 2 ' C ( X ) ≤ 3 and if | X | > 2 then girth Γ 2 ' C ( X ) = 3 . We give some topological properties of X equivalent to graph properties of Γ 2 ' C ( X ) . Finally we have proved that X is an almost P -space which does not have isolated points if and only if C ( X ) is an almost regular ring...

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