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On completeness in symmetric spaces
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: SeithutiP. MoshokoaIn the literature completeness for symmetric spaces is done through the classical Cauchy criterion for metric spaces. However, unlike the situation in metric spaces a convergent sequence in a symmetric space is not necessarily a Cauchy sequence. In the paper... -
Lattice-Valued Cauchy Spaces and Completion
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Gunther Jäger --- Department of Statistics, South AfricaWe define lattice-valued Cauchy spaces. The category of these spaces is topological over SET and cartesian closed. Special examples are lattice-valued uniform convergence spaces and probabilistic Cauchy spaces. We further define completeness and give a completion for these spaces which... -
SYNTOPOFORMIC SPACES (SYNTOPOGENOUS LIMIT SPACES)
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Dieter Leseberg --- , Federal Republic of GermanyCsászár generalized the uniform spaces, the proximity spaces and the topological spaces to syntopogenous spaces. Cook and Fischer generalized the uniform spaces to uniform limit spaces. Finally Marny generalized the proximity spaces to proximal limit spaces. Analogously we generalize the... -
On convergence completeness in symmetric spaces
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: SeithutiP. MoshokoaThe notion of a convergence complete symmetric space is introduced in [6]. In this paper we shall show that every symmetric space admits a weakly S-convergence complete symmetric space. As applications of convergence completeness, we present some fixed point results... -
Towards a standardized and optimized protocol for rapid biodiversity assessments: spider species richness and assemblage composition in two savanna vegetation types
Item type: Journal Article • Journal: African Zoology • Authors: M.I. Muelelwa --- Centre for Invasion Biology and Department of Zoology, South Africa S.H. Foord --- Centre for Invasion Biology and Department of Zoology, South Africa A.S. Dippenaar-Schoeman --- ARC Plant Protection Research Institute, South Africa E.M. Stam --- National Zoological Gardens of South Africa, South AfricaA semi-quantitative inventory of spider diversity was done in the Blouberg Nature Reserve (BNR) and Western Soutpansberg Conservancy (WSC) situated in the Savanna Biome of the Limpopo Province, South Africa. Two hundred and ninety-six samples of one person-hour work each,... -
Encountering, explaining and refuting essentialism
Item type: Journal Article • Journal: Anthropology Southern Africa • Authors: Jonatan Kurzwelly --- , South Africa Nigel Rapport --- , United Kingdom Andrew D. Spiegel --- , South AfricaEssentialism manifests itself in a diversity of forms and is used in multiple ways. Yet it is always potentially dangerous — even when it is mobilised strategically and in apparently worthy forms for purposes of overcoming oppressive structures. As the... -
Ekeland, Takahashi and Caristi principles in preordered quasi-metric spaces
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: S. Cobzaş --- Babeş-Bolyai University, RomaniaWe prove versions of Ekeland, Takahashi and Caristi principles in pre-ordered quasi-metric spaces, the equivalence between these principles, as well as their equivalence to some completeness results for the underlying quasi-metric space. These extend the results proved in S. Cobzaş,... -
On a class of third-order dissipative differential operator with distributional potentials
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Ji-jun Ao --- Inner Mongolia University of Technology, China Fei-fan Li --- Inner Mongolia University of Technology, ChinaThis paper aims to investigate a class of boundary value problems generated by a third-order differential equation with distributional potentials and some dissipative boundary conditions. We first construct an operator related to the problem, then prove that the operator is...