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 29 Next

Displaying 561 – 580 of 674

Showing per page

Topology and dynamics of unstable attractors

M. A. Morón, J. J. Sánchez-Gabites, J. M. R. Sanjurjo (2007)

Fundamenta Mathematicae

This article aims to explore the theory of unstable attractors with topological tools. A short topological analysis of the isolating blocks for unstable attractors with no external explosions leads quickly to sharp results about their shapes and some hints on how Conley's index is related to stability. Then the setting is specialized to the case of flows in ℝⁿ, where unstable attractors are seen to be dynamically complex since they must have external explosions.

Topology and measure of buried points in Julia sets

Clinton P. Curry, John C. Mayer, E. D. Tymchatyn (2013)

Fundamenta Mathematicae

It is well-known that the set of buried points of a Julia set of a rational function (also called the residual Julia set) is topologically “fat” in the sense that it is a dense G δ if it is non-empty. We show that it is, in many cases, a full-measure subset of the Julia set with respect to conformal measure and the measure of maximal entropy. We also address Hausdorff dimension of buried points in the same cases, and discuss connectivity and topological dimension of the set of buried points. Finally,...

Topology from Neighbourhoods

Roland Coghetto (2015)

Formalized Mathematics

Using Mizar [9], and the formal topological space structure (FMT_Space_Str) [19], we introduce the three U-FMT conditions (U-FMT filter, U-FMT with point and U-FMT local) similar to those VI, VII, VIII and VIV of the proposition 2 in [10]: If to each element x of a set X there corresponds a set B(x) of subsets of X such that the properties VI, VII, VIII and VIV are satisfied, then there is a unique topological structure on X such that, for each x ∈ X, B(x) is the set of neighborhoods of x in this...

Topology of the isometry group of the Urysohn space

Julien Melleray (2010)

Fundamenta Mathematicae

Using classical results of infinite-dimensional geometry, we show that the isometry group of the Urysohn space, endowed with its usual Polish group topology, is homeomorphic to the separable Hilbert space ℓ²(ℕ). The proof is based on a lemma about extensions of metric spaces by finite metric spaces, which we also use to investigate (answering a question of I. Goldbring) the relationship, when A,B are finite subsets of the Urysohn space, between the group of isometries fixing A pointwise, the group...

Topology on ordered fields

Yoshio Tanaka (2012)

Commentationes Mathematicae Universitatis Carolinae

An ordered field is a field which has a linear order and the order topology by this order. For a subfield F of an ordered field, we give characterizations for F to be Dedekind-complete or Archimedean in terms of the order topology and the subspace topology on F .

Total negation under constraint: pre-anti properties

T. Brian M. McMaster, Colin R. Turner (2000)

Bollettino dell'Unione Matematica Italiana

L'operazione «anti( )» di Paul Bankston fu introdotta in contesto della famiglia di tutti gli spazii topologici. Però, per molte ricerche ci conviene lavorare esclusivamente in una classe costretta di spazii di cui la struttura e ricca abbastanza di facilitare il ragionamento. In quest'articolo descriviamo come trasferire anti ( ), e concetti allacciati, dentro una tale classe costretta; con riferimento speciale all'esistenza di «pre-antis».

Totally bounded frame quasi-uniformities

Peter Fletcher, Worthen N. Hunsaker, William F. Lindgren (1993)

Commentationes Mathematicae Universitatis Carolinae

This paper considers totally bounded quasi-uniformities and quasi-proximities for frames and shows that for a given quasi-proximity ◃ on a frame L there is a totally bounded quasi-uniformity on L that is the coarsest quasi-uniformity, and the only totally bounded quasi-uniformity, that determines ◃ . The constructions due to B. Banaschewski and A. Pultr of the Cauchy spectrum ψ L and the compactification ℜ L of a uniform frame ( L , 𝐔 ) are meaningful for quasi-uniform frames. If 𝐔 is a totally bounded quasi-uniformity...

Totally Brown subsets of the Golomb space and the Kirch space

José del Carmen Alberto-Domínguez, Gerardo Acosta, Gerardo Delgadillo-Piñón (2022)

Commentationes Mathematicae Universitatis Carolinae

A topological space X is totally Brown if for each n ∈ ℕ ∖ { 1 } and every nonempty open subsets U 1 , U 2 , ... , U n of X we have cl X ( U 1 ) ∩ cl X ( U 2 ) ∩ ⋯ ∩ cl X ( U n ) ≠ ∅ . Totally Brown spaces are connected. In this paper we consider the Golomb topology τ G on the set ℕ of natural numbers, as well as the Kirch topology τ K on ℕ . Then we examine subsets of these spaces which are totally Brown. Among other results, we characterize the arithmetic progressions which are either totally Brown or totally separated in ( ℕ , τ G ) . We also show that ( ℕ , τ G ) and ( ℕ , τ K ) are aposyndetic. Our results...

Currently displaying 561 – 580 of 674