The Study of the Concept of Q*Compact Spaces
Ibrahim Bassi,
Yakubu Gabriel,
Onuk Oji Galadima
Issue:
Volume 7, Issue 1, February 2018
Pages:
1-5
Received:
24 October 2017
Accepted:
15 November 2017
Published:
2 February 2018
Abstract: The aim of this research is to extend the new type of compact spaces called Q* compact spaces, study its properties and generate new results of the space. It investigate the Q*-compactness of topological spaces with separable, Q*-metrizable, Q*-Hausdorff, homeomorphic, connected and finite intersection properties. The closed interval [0, 1] is Q* compact. So, it is deduced that the closed interval [0, 1] is Q*-compact. For example, if (X, τ) = ℝ and A = (0, ∞) then A is not Q*-compact. A subset S of ℝ is Q*-compact. Also, if (X, τ) is a Q*-compact metrizable space. Then (X, τ) is separable. (Y, τ1) is Q*-compact and metrizable if f is a continuous mapping of a Q*-compact metric space (X, d) onto a Q*-Hausdorff space (Y, τ1). An infinite subset of a Q*-compact space must have a limit point. The continuous mapping of a Q*-compact space has a greatest element and a least element. Eleven theorems were considered and their results were presented accordingly.
Abstract: The aim of this research is to extend the new type of compact spaces called Q* compact spaces, study its properties and generate new results of the space. It investigate the Q*-compactness of topological spaces with separable, Q*-metrizable, Q*-Hausdorff, homeomorphic, connected and finite intersection properties. The closed interval [0, 1] is Q* c...
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