Réseaux électrique planaires I.
Reseaux électriques planaires II.
Residuality of the set of embeddings into Nagata's n-dimensional universal spaces
Resolutions of spaces and proper inverse systems in shape theory
Resolutions Of Spaces Are Strong Expansions
Retract varieties of monounary algebras
Rétractes Absolus de Voisinage Algébriques
2000 Mathematics Subject Classification: 54C55, 54H25, 55M20.We introduce the class of algebraic ANRs. It is defined by replacing continuous maps by chain mappings in Lefschetz’s characterization of ANRs. To a large extent, the theory of algebraic ANRs parallels the classical theory of ANRs. Every ANR is an algebraic ANR, but the class of algebraic ANRs is much larger; the most striking difference between these classes is that every locally equiconnected metrisable space is an algebraic ANR, whereas...
Retracting fans onto finite fans
Retractions and Open Mappings between Convex Sets.
Rétractions dans les espaces stratifiables
Retracts and homotopies for multi-maps
Retracts in equiconnected spaces.
Retracts of the Sorgenfrey line
Retracts of Tychonoff and normal spaces.
Retral spaces and continua with the fixed point property
We show that every retral continuum with the fixed point property is locally connected. It follows that an indecomposable continuum with the fixed point property is not a retract of a topological group.
Rigid extensions of -groups of continuous functions
Let , and denote the -groups of integer-valued, rational-valued and real-valued continuous functions on a topological space , respectively. Characterizations are given for the extensions to be rigid, major, and dense.
Rigid P-spaces
Ring epimorphisms and .
Rings of continuous functions vanishing at infinity
We prove that a Hausdorff space is locally compact if and only if its topology coincides with the weak topology induced by . It is shown that for a Hausdorff space , there exists a locally compact Hausdorff space such that . It is also shown that for locally compact spaces and , if and only if . Prime ideals in are uniquely represented by a class of prime ideals in . -compact spaces are introduced and it turns out that a locally compact space is -compact if and only if every...
Rings of Real-Valued Continuous Functions. II.