Every weakly initially -compact topological space is pcap
The statement in the title solves a problem raised by T. Retta. We also present a variation of the result in terms of -compactness.
Exactly two-to-one maps from continua onto arc-continua
Continuing studies on 2-to-1 maps onto indecomposable continua having only arcs as proper non-degenerate subcontinua - called here arc-continua - we drop the hypothesis of tree-likeness, and we get some conditions on the arc-continuum image that force any 2-to-1 map to be a local homeomorphism. We show that any 2-to-1 map from a continuum onto a local Cantor bundle Y is either a local homeomorphism or a retraction if Y is orientable, and that it is a local homeomorphism if Y is not orientable.
Exactly two-to-one maps from continua onto some tree-like continua
It is known that no dendrite (Gottschalk 1947) and no hereditarily indecomposable tree-like continuum (J. Heath 1991) can be the image of a continuum under an exactly 2-to-1 (continuous) map. This paper enlarges the class of tree-like continua satisfying this property, namely to include those tree-like continua whose nondegenerate proper subcontinua are arcs. This includes all Knaster continua and Ingram continua. The conjecture that all tree-like continua have this property, stated by S. Nadler...
Example of a convergence commutative group which is not separated
Examples of classical and fuzzy Riesz proximities
Examples of disks in /G which cannot be approximated by P-liftable disks
Examples of fuzzy basic proximities.
Examples of sequential topological groups under the continuum hypothesis
Using CH we construct examples of sequential topological groups: 1. a pair of countable Fréchet topological groups whose product is sequential but is not Fréchet, 2. a countable Fréchet and topological group which contains no copy of the rationals.
Examples relating to mesocompact and sequentially mesocompact spaces
Exchange PF-rings and almost PP-rings.
Exchange PF-rings and almost PP-rings
Exemples d'actions non continues d'un groupe dans un compact.
Existence and approximation of fixed points for set-valued mappings.
Existence and data dependence for multivalued weakly Ćirić-contractive operators.
Existence and data dependence of fixed points and strict fixed points for contractive-type multivalued operators.
Existence of extremal solutions for quadratic fuzzy equations.
Existence of fixed point results in -metric spaces.
Existence of fixed points on compact epilipschitz sets without invariance conditions.
Existence of invariant measures for piecewise continuous transformations
Existence of joins and meets in the partially ordered family of CM-homomorphisms.