All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 3 Next

Displaying 41 – 60 of 267

Showing per page

Separating sets by Darboux-like functions

Aleksander Maliszewski (2002)

Fundamenta Mathematicae

We consider the following problem: Characterize the pairs ⟨A,B⟩ of subsets of ℝ which can be separated by a function from a given class, i.e., for which there exists a function f from that class such that f = 0 on A and f = 1 on B (the classical separation property) or f < 0 on A and f > 0 on B (a new separation property).

Sequential completeness of subspaces of products of two cardinals

Roman Frič, Nobuyuki Kemoto (1999)

Czechoslovak Mathematical Journal

Let κ be a cardinal number with the usual order topology. We prove that all subspaces of κ 2 are weakly sequentially complete and, as a corollary, all subspaces of ω 1 2 are sequentially complete. Moreover we show that a subspace of ( ω 1 + 1 ) 2 need not be sequentially complete, but note that X = A × B is sequentially complete whenever A and B are subspaces of κ .

Sequential continuity on dyadic compacta and topological groups

Aleksander V. Arhangel'skii, Winfried Just, Grzegorz Plebanek (1996)

Commentationes Mathematicae Universitatis Carolinae

We study conditions under which sequentially continuous functions on topological spaces and sequentially continuous homomorphisms of topological groups are continuous.

Sequential convergence in C p ( X )

David H. Fremlin (1994)

Commentationes Mathematicae Universitatis Carolinae

I discuss the number of iterations of the elementary sequential closure operation required to achieve the full sequential closure of a set in spaces of the form C p ( X ) .

Shape index in metric spaces

Francisco R. Ruiz del Portal, José M. Salazar (2003)

Fundamenta Mathematicae

We extend the shape index, introduced by Robbin and Salamon and Mrozek, to locally defined maps in metric spaces. We show that this index is additive. Thus our construction answers in the affirmative two questions posed by Mrozek in [12]. We also prove that the shape index cannot be arbitrarily complicated: the shapes of q-adic solenoids appear as shape indices in natural modifications of Smale's horseshoes but there is not any compact isolated invariant set for any locally defined map in a locally...

Currently displaying 41 – 60 of 267