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Uniformly connected space
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<h2 id="properties">Properties</h2> <p>A <a href="/facts/Compact_space/d0cgXJH7">compact</a> <a href="/facts/Uniform_space/GKumHlHo">uniform space</a> is uniformly connected <a href="/facts/If_and_only_if/bYSxGJ66">if and only if</a> it is <a href="/facts/Connected_space/5CUTxfoA">connected</a> </p> <h2 id="examples">Examples</h2> <ul><li>every <a href="/facts/Connected_space/5CUTxfoA">connected space</a> is uniformly connected</li> <li>the <a href="/facts/Rational_number/VJQmyY05">rational numbers</a> and the <a href="/facts/Irrational_numbers/Psv19TET">irrational numbers</a> are disconnected but uniformly connected</li></ul> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/Connectedness/P5w33wdx">connectedness</a></li></ul> <ol><li><a href="/facts/Georg_Cantor/k5v1DvW4">Cantor, Georg</a> <i>Über Unendliche, lineare punktmannigfaltigkeiten</i>, <a href="/facts/Mathematische_Annalen/GPhGaonc">Mathematische Annalen</a>. 21 (1883) 545-591.</li></ol>