Characterization of the continuity of Δ-space via the convergence

DOI

10.2991/978-94-6463-463-1_9How to use a DOI?

Keywords

Δ-convergence; ΔL-convergencd; Δ-space; weak continuous

Abstract

The concepts of Δ-convergence and Δ_L-convergence of a net are introduced in Δ-space defined by Zhang et.al. The characterization of the continuity of the Δ-space is obtained in terms of the Δ-convergence of the nets. The result that the continuity of the Δ-space implies the Δ_L-convergence being topological in Δ-space is given. An example is supplied to illustrate that the converse of the above result does not hold. Meantime, we prove that the Δ-space X is continuous if and only if the Δ_L-convergence is topological in X, X is meet-continuous and  O ( X ) ⋁ ω ( X ) = τ Δ L . Moreover, we put forward the concept of weak continuity of the Δ-space and show that a sufficient and necessary condition for the Δ-space being weak continuous is that the Δ_L-convergence is topological.

Copyright

© 2024 The Author(s)

Open Access

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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TY  - CONF
AU  - Fan Feng
AU  - Qingguo Li
PY  - 2024
DA  - 2024/08/02
TI  - Characterization of the continuity of Δ-space via the convergence
BT  - Proceedings of the International Academic Summer Conference on Number Theory and Information Security (NTIS 2023)
PB  - Atlantis Press
SP  - 122
EP  - 138
SN  - 2352-541X
UR  - https://doi.org/10.2991/978-94-6463-463-1_9
DO  - 10.2991/978-94-6463-463-1_9
ID  - Feng2024
ER  -