A generalization of Banach's contraction principle.
A generalization of boundedly compact metric spaces
A metric space is called a space provided each continuous function on into a metric target space is uniformly continuous. We introduce a class of metric spaces that play, relative to the boundedly compact metric spaces, the same role that spaces play relative to the compact metric spaces.
A generalization of Caristi's fixed point theorem.
A generalization of Čech-complete spaces and Lindelöf -spaces
The class of -spaces is studied in detail. It includes, in particular, all Čech-complete spaces, Lindelöf -spaces, metrizable spaces with the weight , but countable non-metrizable spaces and some metrizable spaces are not in it. It is shown that -spaces are in a duality with Lindelöf -spaces: is an -space if and only if some (every) remainder of in a compactification is a Lindelöf -space [Arhangel’skii A.V., Remainders of metrizable and close to metrizable spaces, Fund. Math. 220 (2013),...
A Generalization of Chain-net Spaces
A generalization of Ćirić quasi-contraction
A generalization of cohomotopy groups
A generalization of component categories
A generalization of fixed point theorems in -metric spaces
A generalization of -compact spaces
A generalization of Kannan's fixed point theorem.
A generalization of Magill's Theorem for non-locally compact spaces
In the theory of compactifications, Magill's theorem that the continuous image of a remainder of a space is again a remainder is one of the most important theorems in the field. It is somewhat unfortunate that the theorem holds only in locally compact spaces. In fact, if all continuous images of a remainder are again remainders, then the space must be locally compact. This paper is a modification of Magill's result to more general spaces. This of course requires restrictions on the nature of the...
A generalization of N. Aronszajn's theorem on connectedness of the fixed point set of a compact mapping
A generalization of Nadler's fixed point theorem.
A generalization of normal spaces
A new class of spaces which contains the class of all normal spaces is defined and its characterization and properties are discussed.
A generalization of perfect maps
A generalization of semiflows on monomials
Let be a field, and the set of monomials of . It is well known that the set of monomial ideals of is in a bijective correspondence with the set of all subsemiflows of the -semiflow . We generalize this to the case of term ideals of , where is a commutative Noetherian ring. A term ideal of is an ideal of generated by a family of terms , where and are integers .
A generalization of Shoenfield theorem on sets
A generalization of Steinhaus' theorem to coordinatewise measure preserving binary transformations
A Generalization of the Strict Topology.