On Fuzzy C-Paracompact Topological Spaces

The aim of this paper is to study fuzzy extensions of some covering properties defined by A. V. Arhangel’skii and studied by other authors. Indeed, in 2016, A. V. Arhangel’skii defined other paracompact-type properties: C-paracompactness and C2-paracompactness. Later, M. M. Saeed, L. Kalantan and H. Alzumi investigated these two properties. In this paper, we define fuzzy extensions of these notions and obtain results about them, and in particular, prove that these are good extensions of those defined by Arhangel’skii

The Encyclopedia of Neutrosophic Researchers - vol. 1

This is the first volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements

Fuzzy topological games, alpha-Metacompactness and alpha-perfect maps

The behavior of Fuzzy Toplogical Games and α-metacompactness under α-perfect maps are studied. Also an attempt is made to bring out some close relationships between Fuzzy Toplogical Games and α-metacompactness

L-fuzzy compactness and related concepts

The compactness defined by Warner and McLean is extended to arbitrary L-fuzzy sets where L is a fuzzy lattice, i.e., a completely distributive lattice with an order reversing involution. It is shown that with our compactness we can build up a satisfactory theory. The different definitions of compactness in L-fuzzy topological spaces are stated and other characterizations of some of these notions are obtained. We also study their goodness and establish the inter-relations between the compactnesses which are good extensions. Good definitions of L-fuzzy regularity and normality are proposed. Following the lines of our compactness we suggest two definitions of L-fuzzy local compactness that are good extensions of the respective ordinary versions. A comparison between them is presented and some of their properties studied. A one point compactification is also obtained. By introducing a new definition of a locally finite family of L-fuzzy sets and combining it with our definition of compactness, we propose an L-fuzzy paracompactness and study some of its properties. Good definitions of L-fuzzy countable and sequential compactness and the Lindelof property are introduced and studied. We also present, in L-fuzzy topological spaces, good extensions of S-closedness and RS-compactness. Some of their properties are examined. Good L-fuzzy versions of almost compactness, near compactness and a strong compactness are put forward and studied. A comparison between these compactness related concepts is also presented

Continuous selections of multivalued mappings

This survey covers in our opinion the most important results in the theory of continuous selections of multivalued mappings (approximately) from 2002 through 2012. It extends and continues our previous such survey which appeared in Recent Progress in General Topology, II, which was published in 2002. In comparison, our present survey considers more restricted and specific areas of mathematics. Note that we do not consider the theory of selectors (i.e. continuous choices of elements from subsets of topological spaces) since this topics is covered by another survey in this volume

Conference Program

Document provides a list of the sessions, speakers, workshops, and committees of the 32nd Summer Conference on Topology and Its Applications

Fuzzy topological spaces

(1) We define normality for fuzzy topological spaces, define a fuzzy unit interval, and prove a Urysohn type lemma. (2) We define uniformities on fuzzy lattices, and characterise uniformizability in terms of complete regularity. (3) We define the product of a collection of fuzzy topological spaces. We define compactness and connectedness, and show that the product is compact (connected) iff each factor space is. (4) We place normality and complete regularity within a coherent hierarchy of separation and regularity axioms. We prove the usual implications, and the usual theorems about compactness and products. (5) We give alternative definitions of uniformities and pseudometrics, and show a compact R1 space has a unique uniformity