Spaces with open countable tightness

Abstract We study topological spaces with open countable tightness introduced by Arhangel’skii. Two characterizations of such spaces are given. Using these characterizations we show that if a topological group G has open countable tightness, then so has its completion and any quotient. The direct locally convex sum of an uncountable family of locally convex spaces does not have open countable tightness. Let Y be a non-trivial metrizable abelian group. It is proved that for every Y -Tychonoff space X , the space $$C_p(X,Y)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi>Y</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> has open countable tightness. Generalizing a result of M. Sakai it is shown that if X is a strongly Y -Tychonoff space, then the space $$C_k(X,Y)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>k</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi>Y</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> has open countable tightness iff every moving off family of compact subsets of X has a countable subfamily which is strongly moving off.