<abstract xmlns="http://www.w3.org/1999/xhtml">Compactification is the process or result of making a topological space into a compact space. An embedding of a topological space <italic>X</italic> as a dense subset of a compact space is called a compactification of <italic>X</italic>. There are a lot of compactification methods but we study with Fan- Gottesman compactification. A topological space <italic>X</italic> is said to be scattered if every nonempty subset <italic>S</italic> of <italic>X</italic> contains at least one point which is isolated in <italic>S</italic>. Compact scattered spaces are important for analysis and topology. In this paper, we investigate the relation between the Fan-Gottesman compactification of <italic>T</italic>3 space and scattered spaces. We show under which conditions the Fan-Gottesman compactification <italic>X</italic>* is a scattered.</abstract>

Compactification is the process or result of making a topological space into a compact space. An embedding of a topological space X as a dense subset of a compact space is called a compactification of X. There are a lot of compactification methods but we study with Fan- Gottesman compactification. A topological space X is said to be scattered if every nonempty subset S of X contains at least one point which is isolated in S. Compact scattered spaces are important for analysis and topology. In this paper, we investigate the relation between the Fan-Gottesman compactification of T3 space and scattered spaces. We show under which conditions the Fan-Gottesman compactification X* is a scattered.

Fan-Gottesman Compactification and Scattered Spaces

Department of Mathematics, Faculty of Science

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Fan-Gottesman Compactification and Scattered Spaces"}

Compactification is the process or result of making a topological space into a compact space. An embedding of a topological space X as a dense subset of a...

Fan-Gottesman Compactification and Scattered Spaces

Published Online: Apr 10, 2020

Page range: 475 - 478

Received: May 13, 2019

Accepted: Jun 13, 2019

DOI: https://doi.org/10.2478/amns.2020.1.00045

Keywords
Fan-Gottesman compactification, Scattered spaces

© 2020 Ceren Sultan Elmali et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fan-Gottesman Compactification and Scattered Spaces

Published Online: Apr 10, 2020

Page range: 475 - 478

Received: May 13, 2019

Accepted: Jun 13, 2019

DOI: https://doi.org/10.2478/amns.2020.1.00045

KeywordsFan-Gottesman compactification, Scattered spaces

© 2020 Ceren Sultan Elmali et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Fan-Gottesman compactification, Scattered spaces