image of a hyperconnected space is hyperconnected. In particular, any continuous function from a hyperconnected space to a Hausdorff space must be constant...

finitely many of the X i {\displaystyle X_{i}} are connected. Every hyperconnected space is locally connected, and connected. The following result follows...

space X {\displaystyle X} , X {\displaystyle X} must be connected, and thus hyperconnected spaces are also connected. Since a simply connected space is...

disconnected and connected. More generally, every hyperconnected space is extremally disconnected. The space on three points with base { { x , y } , { x ,...

See Homotopic maps. Hyperconnected A space is hyperconnected if no two non-empty open sets are disjoint Every hyperconnected space is connected. Identification...

Hyperconnected. A space is hyperconnected if no two non-empty open sets are disjoint. Every hyperconnected space is connected. Ultraconnected. A space is ultraconnected...

topology. The Sierpiński space. A set with the excluded point topology. The right order topology on the real line. Hyperconnected space PlanetMath Steen & Seebach...

{\displaystyle X_{2}} of X . {\displaystyle X.} A topological space is irreducible (or hyperconnected) if it is not reducible. Equivalently, X is irreducible...

{R} } since every such function is constant. The Sierpiński space S is both hyperconnected (since every nonempty open set contains 1) and ultraconnected...

only neighborhood is the whole space X. For example, the particular point topology on a finite space is hyperconnected while the excluded point topology...

hyperconnected, it is pseudocompact. This shows that pseudocompactness doesn't imply any of these other forms of compactness. For a Hausdorff space X...

topological space X {\displaystyle X} is hyperconnected if and only if every nonempty open set is dense in X . {\displaystyle X.} A topological space is submaximal...

normal because no two nonempty open sets are disjoint (that is, it is hyperconnected). The double-pointed cofinite topology is the cofinite topology with...

discrete topology. The cocountable topology on an uncountable set is hyperconnected, thus connected, locally connected and pseudocompact, but neither weakly...

totally disconnected. Hyperconnected but not ultraconnected Every non-empty open set contains p, and hence X is hyperconnected. But if a and b are in...

portmanteau of online and life referring to "the new experience of a hyperconnected reality within which it is no longer sensible to ask whether one may...

entitled Making Space, which documents and explores what it means to be a young person in today's constantly changing, hyperconnected world. Other projects...

Critical Infrastructure Protection group; Hyperconnected World Cross-Industry CEO Session; and Future of Space session. "Ray O. Johnson". www.bvp.com. Retrieved...

Kaine, Time (August 2017). "A New Truman Doctrine: Grand Strategy in a Hyperconnected World". Foreign Affairs. 96 (4): 36–53. "Freedom in the World 2017:...

Economy Jeremy Heimans & Henry Timms, New Power: How Power Works in Our Hyperconnected World - and How to Make It Work for You The longlist was announced 10...

Global’s partnership with Nxera will further support the development of a hyperconnected, AI-ready data centre, enhancing Malaysia's infrastructure for cloud...

consider digital technologies, but the different data flows produced in a hyperconnected society. The datasphere, according to the Datasphere Initiative, was...

California, February 2005.; Anabel Quan-Haase and Barry Wellman. "Hyperconnected Net Work: Computer-Mediated Community in a High-Tech Organization."...

Inclusion 2019 – Museums as Cultural Hubs: The Future of Tradition 2018 – Hyperconnected museum: New approaches, new publics 2017 – Museums and Contested Histories:...

(Abingdon Press, 2008) ISBN 978-0-687-64899-3 Church of Facebook: How the Hyperconnected Are Redefining Community by Jesse Rice (David C. Cook, 2009) ISBN 1-4347-6534-2...

Rainie, L (2012). "Millennials will benefit and suffer due to their hyperconnected lives". Pew Research Center. Catelly, Y. ""TO ALLOW OR NOT TO ALLOW...

"The Global Information Technology Report 2013: Growth and Jobs in a Hyperconnected World" (PDF). World Economic Forum. Geneva. pp. 324–325. Retrieved 5...

Systems (January 2013), World Economic Forum (ed.), Perspectives on a Hyperconnected World: Insights from the Science of Complexity (PDF) (in German) "Modeling...

Omer (2014). "WELCOME TO THE METROPTICON: PROTECTING PRIVACY IN A HYPERCONNECTED TOWN". Fordham Urban Law Journal. 41: 1581. Paskaleva, Krassimira (2013-08-22)...

an n-dimensional virtual world accessible through all of our senses, hyperconnected, endowed with artificial life, and artificial intelligence), where the...