**Seminars and Colloquiums**

for the week of December 10, 2018

for the week of December 10, 2018

*SPEAKERS*

**Wednesday**

Alexandre Karassev, Nipissing University

**Wednesday, 12/12**

**TOPOLOGY/ GEOMETRY SEMINAR**

TITLE: Metrizable remainders of locally compact spaces

SPEAKER: Alexandre Karassev, Nipissing University

TIME: 2:45 PM-3:35 PM (note change)

ROOM: Ayres 120 (note change)

We describe those locally compact noncompact separable metrizable spaces X for which the class R(X) of all metrizable remainders of X consists of all metrizable non-empty compacta. Further, we show that for any pair X and X' of locally compact noncompact connected separable metrizable spaces, either R(X) is a subset R(X') or R(X') is a subset R(X). For each such space X we construct a maximal zero-dimensional metrizable remainder of X that contains any zero-dimensional element of R(X). This allows us to show that the set of classes R(X) for all such X, ordered by inclusion, is isomorphic to first uncountable ordinal. (joint work with Vitalij Chatyrko)

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