Volume 8, Issue 3 (March 2021), Pages: 51-56

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 Original Research Paper

 Title: On the H-space and the product of two H-spaces

 Author(s): Maha M. Saeed ^1, *, Shaza Alawadi ²

 Affiliation(s):

 ¹Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
 ²Department of Mathematics, University of Jeddah, Jeddah, Saudi Arabia

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 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0001-6416-8097

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2021.03.007

 Abstract:

Considering the set of real numbers R, for each x ∈ A, B(x)={(x−ϵ,x+ϵ):ϵ>0}, and for each x∈ R\A, let B(x)={[x,x+ϵ):ϵ>0}, the unique topology generated by {B(x): x ∈ R} is denoted by τ(A) and (R, τ(A)) is called an H-space. In this paper, we give some results about these spaces and the product of two of them, including the separation axioms, wD property, various types of compactness and connectedness, and weaker properties of normality. 

 © 2021 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: 𝐻-space, Sorgenfrey line, Lindelöf, Paracompact, 𝜅-metrizable

 Article History: Received 23 August 2020, Received in revised form 8 November 2020, Accepted 19 November 2020

 Acknowledgment:

No Acknowledgment.

 Compliance with ethical standards

 Conflict of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

 Citation:

  Saeed MM and Alawadi S (2021). On the H-space and the product of two H-spaces. International Journal of Advanced and Applied Sciences, 8(3): 51-56

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