On R-Closed Maps and R-Homeomorphisms in Topological Spaces

Abstract

The aim of this paper is to introduce R-closed maps, R-open maps, R-homeomorphisms, R*-homeomorphisms, strongly R-continuous, perfectly R-continuous and study their properties. Using these new types of maps, several characterizations and properties have been obtained.

The order Zoantharia Rafinesque, 1815 (Cnidaria, Anthozoa: Hexacorallia): supraspecific classification and nomenclature

“…Article 23.9.1.2 of the Code is fulfilled as the family-group name Sphenopidae Hertwig, 1882, is in current and widespread usage, as evidenced by the 30 publications by 99 different authors over the past 34 years using Sphenopidae as a valid name for the taxon it denotes (viz., Nagabhushanam and Jothinayagam 1982: 17; Ryland et al 2000: 191, 192; Ryland and Lancaster 2003: 407, 409, 415; Ryland and Lancaster 2004: 180; Ryland and Westphalen 2004: 411; Ryland et al 2004: 1195, 1197; Acosta et al 2005: 147–149, 151, 154, 160; Sinniger et al 2005: 1122, 1125, 1126; Daly et al 2007: 144; Sinniger et al 2008: 1254, 1256, 1257; Fautin and Daly 2009: 356; Del Mónaco et al 2010: 360; Reimer and Sinniger 2010: 251; Reimer et al 2010c: 606, 616; Swain 2010: 2592; Reimer et al 2011a: 983, 985, 987, 989, 991, 992; Cavallari et al 2012: 25; Longo et al 2012: [1]; Palmer et al 2012: 3880; Reimer et al 2012b: 43, 45, 47, 49; Rodríguez-Viera et al 2012: 32; Costello et al 2013: [2]; Fujii and Reimer 2013: 510, 516; Krishna and Gophane 2013: 210; Koupaei et al 2014: 64; Alencar et al 2015: 1113, 1114, 1121; Irei et al 2015: 1, 2, 4, 6, 14–16, 20; Qin et al 2015: 100; De la Cruz-Francisco et al 2016: 24; Fujii and Reimer 2016: 11, 12, 14, 17, 19, 20; Risi and Macdonald 2016: 113).…”

Developed New Procedure for Low Concentrations of Hydrazine Determination by Spectrophotometry: Hydrazine-Potassium Permanganate System

“…Despite the accuracy of most of the redox methods [9,10] used for the determination of hydrazines, only few are suitable for extremely dilute solutions, and some require carefully controlled conditions. Most of the spectrophotometric procedures available so far in the literatures [11][12][13][14][15][16][17][18][19][20][21][22] are tedious and involve the use of rare and expensive colour reagents. The present work describes a very simple, sensitive and accurate spectrophotometric procedure for the determination of ppm concentrations of hydrazine salts based on reaction with potassium permanganate and measurement of the decolourisation of permanganate.…”

Extended X-ray Absorption Fine Structure (EXAFS) Measurements on Alkali Metal Superatoms of Ta-Atom-Encapsulated Si16 Cage

“…Extensive investigations into the relationship between elements and crystal structures reveal that a single element with a specific atomic radius typically adopts a facecentered cubic lattice or hexagonal closest-packed structure with a coordination number (CN) of 12. 1,2 However, combining two or more elements with different atomic radii, including transition metals, induces changes in the locally close-packed structure, often resulting in a fivefold symmetry or Frank-Kasper (FK) structure with a coordination number of 12 or more. 3−6 The FK structure, also known as a distorted icosahedral (I h ) structure, forms a close-packed structure where the central atom is surrounded by substructures of 12 (I h ), 14, 15, and 16 (T d ) atoms.…”