MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
On $\mathcal{I_{\tau}^{\mathcal{K}}}$-convergence of nets in locally solid Riesz spaces
Pratulananda Das and Ekrem Savaş

Abstract

In this short note we continue our investigation of nets in locally solid Riesz spaces from [P. Das, E. Savas, {On $\mathcal I$-convergence of nets in locally solid Riesz spaces}, Filomat, 27 (1) (2013), 84--89] and introduce the idea of $\Cal{I}_{\tau}^{\Cal{K}}$-convergence of nets which is more general than $\Cal{I}_{\tau}^*$-convergence and obtain some of its basic properties.

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Keywords: Ideal; filter; nets; $\mathcal{I_{\tau}}$-convergence; $\mathcal{I_{\tau}^{\mathcal{K}}}$-convergence; $\mathcal{I_{\tau}^{\mathcal{K}}}$-boundedness; $\mathcal{I}_{\tau}^{\mathcal{K}}$-Cauchy; locally solid Riesz space

MSC: 40G15, 40A35

Pages:  93--99     

Volume  68 ,  Issue  2 ,  2016